Wednesday seminar
Prague Set Theory Seminar
10/12/2021 7:26:40
Dear all,
There is no seminar tomorrow Wednesday October 13th.
The seminar meets again next week on Wednesday October 20th at 11:00 in
the Institute of Mathematics CAS, Zitna 25, seminar room, 3rd floor,
front building.
Program: Noé de Rancourt -- A nonseparable version of Pełczyński's
unconditional space, part 2
Abstract: Pełczyński's unconditional space is a well-known example of a
separable Banach space having a universal unconditional basis. It can be
seen as a Fraïssé limit, and in particular, it has many nontrivial
isometries. In a common work in progress with Ziemowit Kostana, we built
a nonseparable version of this space in a forcing extension.
Surprisingly, unlike its separable counterpart, our space is very rigid.
In my last talk, I presented the motivations of this construction and
the required preliminaries in Banach space theory. In this second talk,
I will concentrate on the actual construction, and the proof of the
rigidity properties, namely:
- every operator on our space is the sum of a diagonal operator and an
operator with separable range;
- all onto isometries of our space are trivial.
As the first talk was mainly classical preliminaries, this talk will be
accessible to those of you who know the basics of Banach space theory
(actually, the theory of unconditional bases), even if they haven't
attended the first talk.
Best,
David
Logic Seminar Wednesday 13 October 2021 16:00 hrs at NUS by Liao Yuke
NUS Logic Seminar
10/11/2021 1:07:48
Invitation to the Logic Seminar at the National University of Singapore
Date: Wednesday, 13 October 2021, 16:00 hrs
Talk via Zoom:
https://nus-sg.zoom.us/j/83049258042?pwd=UWViaWNvTFUrdFdhOHJCdEVydnVkdz09
Meeting ID: 830 4925 8042
Passcode: 1729=x3+y3
Speaker: Liao Yuke
Title: Computable coloring without Pi-3 solution for Hindman's Theorem
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Hindman's theorem is a Ramsey type theorem related to finite sum while
its proof-theoretic strength still has a huge gap. One form of the question
is that if any computable coloring function would have an arithmetic
solution (homogeneous set). We will construct a computable coloring
functions that no Pi-3 set can be homogeneous.
This Week in Logic at CUNY
This Week in Logic at CUNY
10/10/2021 21:24:49
This Week in Logic at CUNY:
- - - - Monday, Oct 11, 2021 - - - -
*** GRAD CENTER CLOSED TODAY ***
- - - - Tuesday, Oct 12, 2021 - - - -Computational Logic SeminarTuesday October 12, 2021, 2-4pmFor a zoom link, contact Sergei Artemov (sartemov@gc.cuny.edu) Speakers:
Rui-Jie Yew, Massachusetts Institute of Technology
Pavel Naumov, University of Southampton, UK
Title: Three Forms of Responsibility in Multiagent Systems
Abstract: In this talk we define and discuss three distinct forms of responsibility in multiagent systems that have been previously considered in the literature: counterfactual responsibility, responsibility for seeing-to-it, and responsibility for forcing. We show that, in the case of the extensive form games, none of these forms can be defined through the other two. In strategic games, the responsibility for seeing-to-it and the responsibility for forcing are equivalent, and their expressibility through the counterfactual responsibility depends on the technical details of the language and the semantics. Finally, we observe that the ownership and the accountability of one agent for another lead to forms of responsibility different from the three that we studied.
- - - - Wednesday, Oct 13, 2021 - - - -
- - - - Thursday, Oct 14, 2021 - - - -
- - - - Friday, Oct 15, 2021 - - - -
Set Theory Seminar
CUNY Graduate Center, Room 6417
Friday, October 1
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (
vgitman@nylogic.org) for meeting id.
Yuxin Zhou University of Florida
Let n>1 be a natural number, let Γn be the hypergraph of isosceles triangles in Rn. Under the axiom of choice, the existence of a countable coloring for Γn is true for every n. Without the axiom of choice, the coloring problems will be hard to answer. We often expect the case that the countable chromatic number of one hypergraph doesn't imply the one for another. With an inaccessible cardinal, there is a model of ZF+DC in which Γ2 has countable chromatic number while Γ3 has uncountable chromatic number. This result is obtained by a balanced forcing over the symmetric Solovay model.
Next Week in Logic at CUNY:
- - - - Monday, Oct 18, 2021 - - - -
Logic and Metaphysics Workshop
Date: Monday, October 4, 4.15-6.15 (NY time)
Rohit Parikh (CUNY GC).
Title: States of Knowledge
Abstract: We know from long ago that among a group of people and given a true proposition P, various states of knowledge of P are possible. The lowest is when no one knows P and the highest is when P is common knowledge. The notion of common knowledge is usually attributed to David Lewis, but it was independently discovered by Schiffer. There are indications of it also in the doctoral dissertation of Robert Nozick. Aumann in his celebrated Agreeing to Disagree paper is generally thought to be the person to introduce it into game theory. But what are the intermediate states? It was shown by Pawel Krasucki and myself that there are only countably many and they correspond to what S. C. Kleene called regular sets. But different states of knowledge can cause different group actions. If you prefer restaurant A to B and so do I, and it is common knowledge, and we want to eat together, then we are likely to both go to A. But without that knowledge we might end up in B, or one in A and one in B. This was discussed by Thomas Schelling who also popularized the notion of focal points. Do different states of knowledge always lead to different group actions? Or can there be distinct states which cannot be distinguished through action? The question seems open. It obviously arises when we try to infer the states of knowledge of animals by witnessing their actions. We will discuss the old developments as well as some more recent ideas.
- - - - Tuesday, Oct 19, 2021 - - - -
- - - - Wednesday, Oct 20, 2021 - - - -
Speaker: Dan Shiebler, Oxford University.
Date and Time: Wednesday October 20, 2021, 7:00 - 8:30 PM., on Zoom.
Title: Out of Sample Generalization with Kan Extensions.
Abstract: A common problem in data science is use this function defined over this small set to generate predictions over that larger set. Extrapolation, interpolation, statistical inference and forecasting all reduce to this problem. The Kan extension is a powerful tool in category theory that generalizes this notion. In this work we explore several applications of Kan extensions to data science.
- - - - Thursday, Oct 21, 2021 - - - -
- - - - Friday, Oct 22, 2021 - - - -
CUNY Graduate Center
Friday, October 22, 2:00-3:30pm
The seminar will take place virtually at 2:00pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting
id. Matthias Aschenbrenner, University of Vienna
- - - - Other Logic News - - - -
- - - - Web Site - - - -
Find us on the web at:
nylogic.github.io(site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to
jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email
jreitz@nylogic.org.
UPDATE - This Week in Logic at CUNY
This Week in Logic at CUNY
10/3/2021 22:48:46
Note the addition of Thursday's talk by Yuri Gurevich in the Philog Seminar.
Best,
Jonas
This Week in Logic at CUNY:
- - - - Monday, Oct 4, 2021 - - - -
Penn Logic and Computation Seminar
Monday, October 4, 3:30 pm US Eastern, online
Speaker: Sergei Artemov, CUNY Graduate Center
Title: Missing Proofs and the Provability of Consistency
Abstract: We argue that there is a class of widely used and readily formalizable arithmetical proofs of universal properties which are not accounted for in the traditional unprovability of consistency analysis. On this basis, we offer a mathematical proof of consistency for Peano Arithmetic PA and demonstrate that this proof is formalizable in PA. This refutes the widespread belief that there exists no consistency proof of a system that can be formalized in the system itself. Gödel’s Second Incompleteness theorem yields that PA cannot derive the consistency formula ConPA. This does not interfere with our formalized proof of PA-consistency which is not a derivation of the consistency formula ConPA.
The link will be available by 12 noon on Monday. To get it, contact Andre Scedrov <
scedrov@math.upenn.edu> or Sergei Artemov <
sartemov@gc.cuny.edu>.
Logic and Metaphysics Workshop
Date: Monday, October 4, 4.15-6.15 (NY time)
Speaker: Yale Weiss (CUNY GC)
Title: Bisemilattice Semantics for Intuitionistic and Relevant Modal Logics
Abstract: In this talk, I consider modal logics extending J (intuitionistic logic) and RMO (sometimes called ‘constructive mingle’). Adapting previous work of Humberstone, all of these systems are given a purely operational bisemilattice semantics and soundness and completeness results are proved. I consider a way of exactly translating each intuitionistic modal system into a relevant modal companion and discuss what, if any, light this sheds on the interpretation of the relevant companions. Various applications are examined (e.g., to developing constructive theories of entailment) and results germane to those applications are proved. I also discuss connections between the present semantic framework and related frameworks, including Fine’s hybrid operational-partial order semantics, inquisitive semantics, and Urquhart’s semilattice semantics.
- - - - Tuesday, Oct 5, 2021 - - - -
Computational Logic Seminar
Tuesday October 5, 2021, 2-4pm
For a zoom link, contact Sergei Artemov (
sartemov@gc.cuny.edu)
Speaker: Noson Yanofsky, CUNYTitle: Diagonalization, Fixed Points, and Self-reference
Abstract: Some of the most profound and famous theorems in mathematics and computer science of the past 150 years can simultaneously be seen as a consequence of diagonalization, as a fixed-point theorem, and as an instance of a self-referential paradox. These results include Cantor's theorems about different levels of infinity; Russell's paradox; Gödel's incompleteness theorem; Turing's halting problem; and much more. Amazingly, all these diverse theorems and all viewpoints can be seen as instances of a single simple theorem of basic category theory. We describe this theorem and show some of the instances. A large part of the talk will be a discussion of diagonalization proofs and fixed point theorems that fail to be instances of this categorical theorem. We will meet another categorical idea that unifies some of those instances. No category theory is needed for this talk.
- - - - Wednesday, Oct 6, 2021 - - - -
Speaker: Gemma De las Cuevas, University of Innsbruck.
Date and Time: Wednesday October 6, 2021, 7:00 - 8:30 PM., on Zoom.
Title: From simplicity to universality and undecidability.
Abstract: Why is it so easy to generate complexity? I will suggest that this is due to the phenomenon of universality — essentially every non-trivial system is universal, and thus able to explore all complexity in its domain. We understand universality in spin models, automata and neural networks. I will present the first step toward rigorously linking the first two, where we cast classical spin Hamiltonians as formal languages and classify the latter in the Chomsky hierarchy. We prove that the language of (effectively) zero-dimensional spin Hamiltonians is regular, one-dimensional spin Hamiltonians is deterministic context-free, and higher-dimensional and all-to-all spin Hamiltonians is context-sensitive. I will also talk about the other side of the coin of universality, namely undecidability, and will raise the question of whether universality is visible in Lawvere’s Theorem.
- - - - Thursday, Oct 7, 2021 - - - -
Philog Seminar
Thursday, October 7, 6:30 PM
A Zoom link will be posted Wednesday on
https://philog.arthurpaulpedersen.org/Negative probabilities: What are they for?
Yuri Gurevich, University of Michigan
The topic may sound nonsensical. The standard frequential interpretation of probabilities makes no sense for negative probabilities. Yet negative probabilities are profitably used in quantum physics and elsewhere. So what are they? What is their intrinsic meaning? We don't know. There are attempts in the literature to provide meaning for negative probabilities but, in our judgement, the problem is wide open.
Instead, we address a more pragmatic question: What are negative probabilities good for? It is not rare in science to use a concept without understanding its intrinsic meaning. Consider early uses of complex numbers. The standard quantitative interpretation of numbers makes no sense for imaginary numbers. And the intrinsic meaning of imaginary numbers wasn't clear (and is debatable even today). Yet complex numbers were profitably used to solve algebraic equations. It turned out, for example, that many real algebraic numbers cannot be
expressed in radicals unless we allow non-real complex coefficients.
It turns out that the disparate quantum applications of negative probabilities can be seen as examples of a certain application template. To make this template explicit, we introduce observation spaces. An observation space S is a family of (nonnegative) probability distributions P1, P2, ... on a common sample space. A question arises whether there is a single probability distribution P (a grounding for S) which yields all P1, P2, ... as marginal distributions. That P may be necessarily signed. We solve the grounding problem for a number of observation spaces of note.
The talk is based on a recent paper with Andreas Blass in J. Phys. A.
- - - - Friday, Oct 8, 2021 - - - -
Set Theory Seminar
CUNY Graduate Center, Room 6417
Friday, October 8
The seminar will take place virtually at 2:00pm US Eastern Standard Time. Please email Victoria Gitman (
vgitman@nylogic.org) for meeting id.
Brent Cody, Virginia Commonwealth UniversityHigher derived topologies
By beginning with the order topology on an ordinal δ, and iteratively declaring more and more derived sets to be open, Bagaria defined the derived topologies τξ on δ, where ξ is an ordinal. He showed that the non-isolated points in the space (δ,τξ) can be characterized using a strong form of iterated simultaneous stationary reflection called ξ-s-reflection, which is deeply connected to certain transfinite indescribability properties. However, Bagaria's definitions break for ξ≥δ because, under his definitions, the δ-th derived topology τδ is discrete and no ordinal α can be α+1-s-stationary. We will discuss some new work in which we use certain diagonal versions of Bagaria's definitions to extend his results. For example, we introduce the notions of diagonal Cantor derivative and use it to obtain a sequence of derived topologies on a regular δ that is strictly longer than that of Bagaria's, under certain hypotheses.
Next Week in Logic at CUNY:
- - - - Monday, Oct 11, 2021 - - - -
- - - - Tuesday, Oct 12, 2021 - - - -
- - - - Wednesday, Oct 13, 2021 - - - -
- - - - Thursday, Oct 14, 2021 - - - -
- - - - Friday, Oct 15, 2021 - - - -
Set Theory Seminar
CUNY Graduate Center, Room 6417
Friday, October 1
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (
vgitman@nylogic.org) for meeting id.
Yuxin Zhou University of Florida
- - - - Other Logic News - - - -
- - - - Web Site - - - -
Find us on the web at:
nylogic.github.io(site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to
jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email
jreitz@nylogic.org.
This Week in Logic at CUNY
This Week in Logic at CUNY
10/3/2021 18:35:33
This Week in Logic at CUNY:
- - - - Monday, Oct 4, 2021 - - - -
Penn Logic and Computation Seminar
Monday, October 4, 3:30 pm US Eastern, online
Speaker: Sergei Artemov, CUNY Graduate Center
Title: Missing Proofs and the Provability of Consistency
Abstract: We argue that there is a class of widely used and readily formalizable arithmetical proofs of universal properties which are not accounted for in the traditional unprovability of consistency analysis. On this basis, we offer a mathematical proof of consistency for Peano Arithmetic PA and demonstrate that this proof is formalizable in PA. This refutes the widespread belief that there exists no consistency proof of a system that can be formalized in the system itself. Gödel’s Second Incompleteness theorem yields that PA cannot derive the consistency formula ConPA. This does not interfere with our formalized proof of PA-consistency which is not a derivation of the consistency formula ConPA.
The link will be available by 12 noon on Monday. To get it, contact Andre Scedrov <
scedrov@math.upenn.edu> or Sergei Artemov <
sartemov@gc.cuny.edu>.
Logic and Metaphysics Workshop
Date: Monday, October 4, 4.15-6.15 (NY time)
Speaker: Yale Weiss (CUNY GC)
Title: Bisemilattice Semantics for Intuitionistic and Relevant Modal Logics
Abstract: In this talk, I consider modal logics extending J (intuitionistic logic) and RMO (sometimes called ‘constructive mingle’). Adapting previous work of Humberstone, all of these systems are given a purely operational bisemilattice semantics and soundness and completeness results are proved. I consider a way of exactly translating each intuitionistic modal system into a relevant modal companion and discuss what, if any, light this sheds on the interpretation of the relevant companions. Various applications are examined (e.g., to developing constructive theories of entailment) and results germane to those applications are proved. I also discuss connections between the present semantic framework and related frameworks, including Fine’s hybrid operational-partial order semantics, inquisitive semantics, and Urquhart’s semilattice semantics.
- - - - Tuesday, Oct 5, 2021 - - - -
Computational Logic Seminar
Tuesday October 5, 2021, 2-4pm
For a zoom link, contact Sergei Artemov (
sartemov@gc.cuny.edu)
Speaker: Noson Yanofsky, CUNYTitle: Diagonalization, Fixed Points, and Self-reference
Abstract: Some of the most profound and famous theorems in mathematics and computer science of the past 150 years can simultaneously be seen as a consequence of diagonalization, as a fixed-point theorem, and as an instance of a self-referential paradox. These results include Cantor's theorems about different levels of infinity; Russell's paradox; Gödel's incompleteness theorem; Turing's halting problem; and much more. Amazingly, all these diverse theorems and all viewpoints can be seen as instances of a single simple theorem of basic category theory. We describe this theorem and show some of the instances. A large part of the talk will be a discussion of diagonalization proofs and fixed point theorems that fail to be instances of this categorical theorem. We will meet another categorical idea that unifies some of those instances. No category theory is needed for this talk.
- - - - Wednesday, Oct 6, 2021 - - - -
Speaker: Gemma De las Cuevas, University of Innsbruck.
Date and Time: Wednesday October 6, 2021, 7:00 - 8:30 PM., on Zoom.
Title: From simplicity to universality and undecidability.
Abstract: Why is it so easy to generate complexity? I will suggest that this is due to the phenomenon of universality — essentially every non-trivial system is universal, and thus able to explore all complexity in its domain. We understand universality in spin models, automata and neural networks. I will present the first step toward rigorously linking the first two, where we cast classical spin Hamiltonians as formal languages and classify the latter in the Chomsky hierarchy. We prove that the language of (effectively) zero-dimensional spin Hamiltonians is regular, one-dimensional spin Hamiltonians is deterministic context-free, and higher-dimensional and all-to-all spin Hamiltonians is context-sensitive. I will also talk about the other side of the coin of universality, namely undecidability, and will raise the question of whether universality is visible in Lawvere’s Theorem.
- - - - Thursday, Oct 7, 2021 - - - -
- - - - Friday, Oct 8, 2021 - - - -
Set Theory Seminar
CUNY Graduate Center, Room 6417
Friday, October 8
The seminar will take place virtually at 2:00pm US Eastern Standard Time. Please email Victoria Gitman (
vgitman@nylogic.org) for meeting id.
Brent Cody, Virginia Commonwealth UniversityHigher derived topologies
By beginning with the order topology on an ordinal δ, and iteratively declaring more and more derived sets to be open, Bagaria defined the derived topologies τξ on δ, where ξ is an ordinal. He showed that the non-isolated points in the space (δ,τξ) can be characterized using a strong form of iterated simultaneous stationary reflection called ξ-s-reflection, which is deeply connected to certain transfinite indescribability properties. However, Bagaria's definitions break for ξ≥δ because, under his definitions, the δ-th derived topology τδ is discrete and no ordinal α can be α+1-s-stationary. We will discuss some new work in which we use certain diagonal versions of Bagaria's definitions to extend his results. For example, we introduce the notions of diagonal Cantor derivative and use it to obtain a sequence of derived topologies on a regular δ that is strictly longer than that of Bagaria's, under certain hypotheses.
Next Week in Logic at CUNY:
- - - - Monday, Oct 11, 2021 - - - -
- - - - Tuesday, Oct 12, 2021 - - - -
- - - - Wednesday, Oct 13, 2021 - - - -
- - - - Thursday, Oct 14, 2021 - - - -
- - - - Friday, Oct 15, 2021 - - - -
Set Theory Seminar
CUNY Graduate Center, Room 6417
Friday, October 1
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (
vgitman@nylogic.org) for meeting id.
Yuxin Zhou University of Florida
- - - - Other Logic News - - - -
- - - - Web Site - - - -
Find us on the web at:
nylogic.github.io(site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to
jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email
jreitz@nylogic.org.
(KGRC) Set Theory Research Seminar talk on Tuesday, October 5
Kurt Godel Research Center
10/1/2021 15:10:00
The KGRC welcomes as guest:
Vladimir Tkachuk (host: Vera Fischer) will visit from October 3 to October 6
and give a talk (see below).
* * *
Set Theory Research Seminar
Kurt Gödel Research Center
Tuesday, October 5
"Exponential domination and its bidual in function spaces"
Vladimir Tkachuk
(Universidad Autonoma Metropolitana, Mexico City, Mexico)
Given an infinite cardinal \kappa, we say that a space X features exponential
\kappa-domination if every set A \subset X with |A| \leq 2^\kappa is contained
in the closure of a set of cardinality \leq \kappa. Evidently, every space X of
density not exceeding \kappa features exponential \kappa-domination. We will
show that spaces with exponential \kappa-domination constitute a class with
nice categorical properties and, in Cech-complete spaces, exponential
\kappa-domination coincides with density \leq \kappa. Another merit of
exponential \kappa-domination is that it has a bidual in function spaces. To
show this, we will introduce exponential \kappa-cofinality and prove that X is
exponentially \kappa-cofinal if and only if Cp(X) features exponential
\kappa-domination and X is a space with exponential \kappa-domination if and
only if Cp(X) is exponentially \kappa-cofinal.
Time and Place
Talk at 3:00pm, in person
Universität Wien
Institut für Mathematik
Lecture Hall HS 8
1st floor
Oskar-Morgenstern-Platz 1
1090 Wien
Please be aware of the fact that you may be required to show proof of your 3G
status upon entry of the buildings, or during sporadic random checks in the
seminar rooms. During the Logic Colloquium we will also pass around an
attendance sheet to facilitate contact tracing. (According to the regulations,
this form will be kept for 28 days and destroyed thereafter.)
Two events on October 5
Carnegie Mellon Logic Seminar
10/1/2021 13:22:19
TUESDAY, October 5, 2021
Mathematical logic seminar: 3:30 P.M., Online, Jindra Zapletal,
University of Florida
Zoom link:
https://cmu.zoom.us/j/621951121?pwd=eWEwVit5WUxlUExOWE51ajdFZnJ2Zz09
Meeting ID: 621 951 121
Passcode: 617076
TITLE: Set theory of algebraic hypergraphs
ABSTRACT: I explain the main aim of the geometric set theory program:
obtaining a careful calibration of Sigma two one sentences (typically,
consequences of the axiom of choice) in choiceless set theory. As a
specific class of such sentences, I consider the countable chromatic
number of various (sigma-)algebraic hypergraphs on Euclidean spaces. A
recent result deals with the graph G_n connecting points of rational
distance in R^n: for every n>0, it is consistent with ZF+DC that the
chromatic number of G_n is countable while that of G_{n+1} is not.
TUESDAY, October 5, 2021
Set Theory Reading Group: 4:30 P.M., Online, Yuxin Zhou, University of
Florida
Zoom link:
https://cmu.zoom.us/j/621951121?pwd=eWEwVit5WUxlUExOWE51ajdFZnJ2Zz09
Meeting ID: 621 951 121
Passcode: 617076
TITLE: Distinguish coloring problems for isosceles triangle in R^2 and R^3
ABSTRACT: For n a positive natural number, let Γn be the hypergraph of
isosceles triangles in R^n. Under the axiom of choice, the existence of a
countable coloring for Γn is true for every n. Without the axiom of
choice, the coloring problems will be hard to answer. With the existence
of the inaccessible cardinal assumption, there is a model of ZF+DC in
which Γ2 has countable chromatic number while Γ3 has uncountable chromatic
number. This result is obtained by forcing over the symmetric Solovay
model.
Wednesday seminar
Prague Set Theory Seminar
10/1/2021 3:20:28
Dear all,
The seminar meets on Wednesday October 6th at 11:00 in the Institute of
Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.
Program: Noé de Rancourt -- A nonseparable version of Pełczyński's
unconditional space
Abstract: Pełczyński's unconditional space is a well-known example of a
separable Banach space having a universal unconditional basis. It can be
seen as a Fraïssé limit, and in particular, it has many nontrivial
isometries. In a common work in progress with Ziemowit Kostana, we built
a nonseparable version of this space in a forcing extension.
Surprisingly, unlike its separable counterpart, our space is very rigid.
In this talk, I will explain the construction of this space, show that
it has few operators, and that all of its isometries are trivial.
I will not assume any knowledge in Banach space theory, apart from a
vague idea of what a Banach space is. The construction and the proofs I
will present rely on almost no prerequisites in functional analysis, so
I will be able to introduce everything during the talk.
Best,
David
Logic Seminar 6 Oct 2021 16:00 hrs at NUS by Chong Chitat
NUS Logic Seminar
10/1/2021 1:25:33
Invitation to the Logic Seminar at the National University of Singapore
Date: Wednesday, 6 October 2021, 16:00 hrs
Talk via Zoom:
https://nus-sg.zoom.us/j/83049258042?pwd=UWViaWNvTFUrdFdhOHJCdEVydnVkdz09
Meeting ID: 830 4925 8042
Passcode: 1729=x3+y3
Speaker: Chong Chitat
Title: First-order strength of tree colorings
Abstract:
In this talk we discuss the proof-theoretic strength, from the reverse
mathematics perspective, of combinatorial principles concerning the
coloring of binary trees and finite products of binary trees.
Beginning with the principle TT^1, which states that every finite
coloring of the full binary tree has an isomorphic monochromatic
subtree, we will cover its strengthening to the existence of a strong
monochromatic subtree, and to the full generalization of the latter
known as the Halpern-Laeuchli Theorem.
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
This Week in Logic at CUNY - UPDATE
This Week in Logic at CUNY
9/27/2021 21:28:21
Hi everyone,
Please see the addition of tomorrow's (Tuesday 9/28) talk in the Computational Logic Seminar.
Best,
Jonas
This Week in Logic at CUNY:
- - - - Tuesday, Sep 28, 2021 - - - -
Computational Logic Seminar
Tuesday September 28, 2021, 2-4pm
For a zoom link, contact Sergei Artemov (
sartemov@gc.cuny.edu)
Speaker: Melvin Fitting, CUNY Graduate Center
Title: Admitting the Empty Domain
Abstract. Classical logic is almost always formulated with the empty domain not allowed. Still, we do understand quantification over the empty domain. So why the discrepancy? Allowing the empty domain was investigated axiomatically by a couple of well-known people in the 1950’s and 1960’s, but this had no real effect. It turns out there are two versions of what is called “Inclusive” logic, allowing the empty domain. I looked at this using tableaus, 50 years ago, and found that the difference between the two versions was easy to understand with tableau machinery. Recently I went back and looked at the work again, and found that the two versions actually differ on interpolation. One version has interpolants, the other doesn’t. A curious result, certainly..
This talk is about classical logic. But the same issues come up for intuitionistic logic, modal logics, paraconsistent logics, and so on. Nobody seems to have looked at what happens. At the heart of it all, the original question that prompted the investigations of the 1960’s still remains: why should the existence of something be taken as a logical truth?
- - - - Wednesday, Sep 29, 2021 - - - -
- - - - Thursday, Sep 30, 2021 - - - -
- - - - Friday, Oct 01, 2021 - - - -
Set Theory Seminar
CUNY Graduate Center, Room 6417
Friday, October 1
The seminar will take place virtually at 11:30am US Eastern Standard Time. Please email Victoria Gitman (
vgitman@nylogic.org) for meeting id.
Matteo Viale, University of Torino
Absolute model companionship, forcibility, and the continuum problem: Part II
Absolute model companionship (AMC) is a strengthening of model companionship defined as follows: For a theory T, T∃∨∀ denotes the logical consequences of T which are boolean combinations of universal sentences. T∗ is the AMC of T if it is model complete and T∃∨∀=T∗∃∨∀. The {+,⋅,0,1}-theory ACF of algebraically closed field is the model companion of the theory of Fields but not its AMC as ∃x(x2+1=0)∈ACF∃∨∀∖Fields∃∨∀. Any model complete theory T is the AMC of T∃∨∀. We use AMC to study the continuum problem and to gauge the expressive power of forcing. We show that (a definable version of) 2ℵ0=ℵ2 is the unique solution to the continuum problem which can be in the AMC of a partial Morleyization of the ∈-theory ZFC+there are class many supercompact cardinals. We also show that (assuming large cardinals) forcibility overlaps with the apparently weaker notion of consistency for any mathematical problem ψ expressible as a Π2-sentence of a (very large fragment of) third order arithmetic (CH, the Suslin hypothesis, the Whitehead conjecture for free groups are a small sample of such problems ψ). Partial Morleyizations can be described as follows: let Formτ be the set of first order τ-formulae; for A⊆Formτ, τA is the expansion of τ adding atomic relation symbols Rϕ for all formulae ϕ in A and Tτ,A is the τA-theory asserting that each τ-formula ϕ(→x)∈A is logically equivalent to the corresponding atomic formula Rϕ(→x). For a τ-theory T T+Tτ,A is the partial Morleyization of T induced by A⊆Formτ.
Next Week in Logic at CUNY:
- - - - Monday, Oct 4, 2021 - - - -
Logic and Metaphysics Workshop
Date: Monday, October 4, 4.15-6.15 (NY time)
Rushed Ahmad, UConn
- - - - Tuesday, Oct 5, 2021 - - - -
- - - - Wednesday, Oct 6, 2021 - - - -
- - - - Thursday, Oct 7, 2021 - - - -
- - - - Friday, Oct 8, 2021 - - - -
Set Theory Seminar
CUNY Graduate Center, Room 6417
Friday, October 8
The seminar will take place virtually at 2:00pm US Eastern Standard Time. Please email Victoria Gitman (
vgitman@nylogic.org) for meeting id.
Brent Cody, Virginia Commonwealth UniversityHigher derived topologies- - - - Other Logic News - - - -
ANNOUNCEMENT - Carl Posy - Working Group on Intuitionism
I am assembling a working group on intuitionism. We aim eventually to explore the philosophical ground of intuitionistic mathematics. We will ultimately look at issues in philosophy of mind (including phenomenology), epistemology, ontology and semantics. However, in order to do so, we will begin with in depth studies of intuitionistic mathematics and intuitionistic logic.
Participation in the group will provide the needed background for someone who would like to develop large or small projects related to some aspect of intuitionism (mathematics, logic or philosophy). The group will also serve those who are interested simply in acquiring a working knowledge of intuitionism per se.
Our initial studies of intuitionistic mathematics and logic will roughly follow the organization of the first chapters of my recent book Mathematical Intuitionism. However, we will refine, correct and expand the material in the book. There’ll be references and material for those who would like to pursue some topic or other even further.
The group invites both participants with some limited or even extensive background in intuitionism and those without any background in intuitionism but with an interest in learning about intuitionism and/or working on related research aims. Some knowledge of mathematics (in particular of elementary real analysis) and/or logic (in particular through basic philosophical logic) is desirable.
The group will have regularly scheduled meetings no more frequently than twice a month, during the academic year. We will set a schedule at the start of each year.
The current plan is to function for at least two or three academic years. Sometime in the second or third year we will have a conference including members and outside researchers. We will begin in late 2021 or early 2022.
From time to time will also have guest lectures from prominent researchers.
From time to time active members will prepare and present material -- appropriate to their background and interests.
Anyone interested should contact me at:
carl.posy@mail.huji.ac.il We will then arrange a time to speak.
- - - - Web Site - - - -
Find us on the web at:
nylogic.github.io(site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to
jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email
jreitz@nylogic.org.
This Week in Logic at CUNY
This Week in Logic at CUNY
9/26/2021 22:20:40
Hi everyone,
Apologies for the late start this semester. Regular weekly mailings of "This Week in Logic" will continue going forward - please send me your announcements for upcoming New York logic events. Welcome back!
Best,
Jonas
This Week in Logic at CUNY:
- - - - Monday, Sep 27, 2021 - - - -
Logic and Metaphysics Workshop
Date: Monday, September 27, 4.15-6.15 (NY time)
Speaker: Rashed Ahmad (University of Connecticut)
Title: A Recipe for Paradox: A Better Schema than the Inclosure Schema
Abstract: In this talk, we provide a recipe that not only captures the common structure between semantic paradoxes but it also captures our intuitions regarding the relations between these paradoxes. Before we unveil our recipe, we first talk about a popular schema introduced by Graham Priest, namely, the inclosure schema. Without rehashing previous arguments against the inclosure schema, we contribute different arguments for the same concern that the inclosure schema bundles the wrong paradoxes together. That is, we will provide alternative arguments on why the inclosure schema is both too broad for including the Sorites paradox, and too narrow for excluding Curry’s paradox. We then spell out our recipe. Our recipe consists of three ingredients: (1) a predicate that has two specific rules, (2) a simple method to find a partial negative modality, and (3) a diagonal lemma that would allow us to let sentences be their partial negative modalities. The recipe shows that all of the following paradoxes share the same structure: The liar, Curry’s paradox, Validity Curry, Provability Liar, a paradox leading to Löb’s theorem, Knower’s paradox, Knower’s Curry, Grelling-Nelson’s paradox, Russell’s paradox in terms of extensions, alternative liar and alternative Curry, and other unexplored paradoxes. We conclude the talk by stating the lessons that we can learn from the recipe, and what kind of solutions does the recipe suggest if we want to adhere to the Principle of Uniform Solution.
- - - - Tuesday, Sep 28, 2021 - - - -
- - - - Wednesday, Sep 29, 2021 - - - -
- - - - Thursday, Sep 30, 2021 - - - -
- - - - Friday, Oct 01, 2021 - - - -
Set Theory Seminar
CUNY Graduate Center, Room 6417
Friday, October 1
The seminar will take place virtually at 11:30am US Eastern Standard Time. Please email Victoria Gitman (
vgitman@nylogic.org) for meeting id.
Matteo Viale, University of Torino
Absolute model companionship, forcibility, and the continuum problem: Part II
Absolute model companionship (AMC) is a strengthening of model companionship defined as follows: For a theory T, T∃∨∀ denotes the logical consequences of T which are boolean combinations of universal sentences. T∗ is the AMC of T if it is model complete and T∃∨∀=T∗∃∨∀. The {+,⋅,0,1}-theory ACF of algebraically closed field is the model companion of the theory of Fields but not its AMC as ∃x(x2+1=0)∈ACF∃∨∀∖Fields∃∨∀. Any model complete theory T is the AMC of T∃∨∀. We use AMC to study the continuum problem and to gauge the expressive power of forcing. We show that (a definable version of) 2ℵ0=ℵ2 is the unique solution to the continuum problem which can be in the AMC of a partial Morleyization of the ∈-theory ZFC+there are class many supercompact cardinals. We also show that (assuming large cardinals) forcibility overlaps with the apparently weaker notion of consistency for any mathematical problem ψ expressible as a Π2-sentence of a (very large fragment of) third order arithmetic (CH, the Suslin hypothesis, the Whitehead conjecture for free groups are a small sample of such problems ψ). Partial Morleyizations can be described as follows: let Formτ be the set of first order τ-formulae; for A⊆Formτ, τA is the expansion of τ adding atomic relation symbols Rϕ for all formulae ϕ in A and Tτ,A is the τA-theory asserting that each τ-formula ϕ(→x)∈A is logically equivalent to the corresponding atomic formula Rϕ(→x). For a τ-theory T T+Tτ,A is the partial Morleyization of T induced by A⊆Formτ.
Next Week in Logic at CUNY:
- - - - Monday, Oct 4, 2021 - - - -
Logic and Metaphysics Workshop
Date: Monday, October 4, 4.15-6.15 (NY time)
Rushed Ahmad, UConn
- - - - Tuesday, Oct 5, 2021 - - - -
- - - - Wednesday, Oct 6, 2021 - - - -
- - - - Thursday, Oct 7, 2021 - - - -
- - - - Friday, Oct 8, 2021 - - - -
Set Theory Seminar
CUNY Graduate Center, Room 6417
Friday, October 8
The seminar will take place virtually at 2:00pm US Eastern Standard Time. Please email Victoria Gitman (
vgitman@nylogic.org) for meeting id.
Brent Cody, Virginia Commonwealth UniversityHigher derived topologies- - - - Other Logic News - - - -
ANNOUNCEMENT - Carl Posy - Working Group on Intuitionism
I am assembling a working group on intuitionism. We aim eventually to explore the philosophical ground of intuitionistic mathematics. We will ultimately look at issues in philosophy of mind (including phenomenology), epistemology, ontology and semantics. However, in order to do so, we will begin with in depth studies of intuitionistic mathematics and intuitionistic logic.
Participation in the group will provide the needed background for someone who would like to develop large or small projects related to some aspect of intuitionism (mathematics, logic or philosophy). The group will also serve those who are interested simply in acquiring a working knowledge of intuitionism per se.
Our initial studies of intuitionistic mathematics and logic will roughly follow the organization of the first chapters of my recent book Mathematical Intuitionism. However, we will refine, correct and expand the material in the book. There’ll be references and material for those who would like to pursue some topic or other even further.
The group invites both participants with some limited or even extensive background in intuitionism and those without any background in intuitionism but with an interest in learning about intuitionism and/or working on related research aims. Some knowledge of mathematics (in particular of elementary real analysis) and/or logic (in particular through basic philosophical logic) is desirable.
The group will have regularly scheduled meetings no more frequently than twice a month, during the academic year. We will set a schedule at the start of each year.
The current plan is to function for at least two or three academic years. Sometime in the second or third year we will have a conference including members and outside researchers. We will begin in late 2021 or early 2022.
From time to time will also have guest lectures from prominent researchers.
From time to time active members will prepare and present material -- appropriate to their background and interests.
Anyone interested should contact me at:
carl.posy@mail.huji.ac.il We will then arrange a time to speak.
- - - - Web Site - - - -
Find us on the web at:
nylogic.github.io(site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to
jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email
jreitz@nylogic.org.
Two events on Tuesday 9/28/21
Carnegie Mellon Logic Seminar
9/24/2021 18:43:53
TUESDAY, September 28, 2021
Mathematical logic seminar: 3:30 P.M., Online, Thomas Gilton, University
of Pittsburgh
Zoom link:
https://cmu.zoom.us/j/621951121?pwd=eWEwVit5WUxlUExOWE51ajdFZnJ2Zz09
Meeting ID: 621 951 121
Passcode: 617076
TITLE: The tension between reflection/compactness and rigidity in
combinatorial set theory
ABSTRACT: The aim of this talk is to provide background with which to
motivate a recent joint result of the speaker with Omer Ben-Neria. This
result concerns the tension between two classes of combinatorial
principles in set theory, namely reflection/compactness principles on the
one hand and incompactness/anti-reflection properties on the other. The
rigidity implied by the latter class often suffices to prove the negation
of principles in the former class, and as a result, a large research
program in set theory is dedicated to investigating when principles from
these two classes are jointly consistent. Our theorem - that the Special
Aronszajn Tree Property is consistent with Club Stationary Reflection on
$\omega_2$ - is such a result. We will discuss this tension historically
before showing how, in our result, the tension shows up in our proof,
especially in the radically different properties of our posets which we
have to maintain throughout the course of our construction.
TUESDAY, September 28, 2021
Set Theory Reading Group: 4:30 P.M., Online, Thomas Gilton, University of
Pittsburgh
Zoom link:
https://cmu.zoom.us/j/621951121?pwd=eWEwVit5WUxlUExOWE51ajdFZnJ2Zz09
Meeting ID: 621 951 121
Passcode: 617076
TITLE: Club stationary reflection and the special Aronszajn tree property
ABSTRACT: In this talk, we will dive into the technical details of our
result with Omer Ben-Neria. We will first show how to specialize trees on
$\omega_2$ with a preparatory forcing which is no longer $\kappa$-c.c., as
in the classic setting of Laver and Shelah. Rather, this preparatory
forcing will satisfy a kind of $\kappa$-strong properness which is
witnessed by continuous residue functions like those used in various side
conditions iteration theorems of Itay Neeman. We then show how to build
posets satisfying this kind of $\kappa$-strong properness by following a
Levy collapse of a weakly compact with a class of posets we call
$\mathcal{F}_{WC}$-completely proper, where $\mathcal{F}_{WC}$ is the
weakly compact filter. This is similar to Abraham's use of guiding reals
to obtain strong properness for countable models. We then close by
gesturing to solutions of the technical problems which remain,
particularly ones involving new preservation theorems for Aronszajn trees
and stationary sets.
Barcelona Set theory Seminar
Barcelona Logic Seminar
9/24/2021 9:47:03
Dear All,
Please find attached the announcement of the next session of the Barcelona Set Theory Seminar. Feel free to distribute it.
SPEAKER: Zhixing You (Universitat de Barcelona)
TITLE:
DATE: 29 September 2021
TIME: 16:00 (CEST)
PLACE: The Seminar will take place online via Zoom:
Meeting ID: 985 6524 7347
Passcode: 243408
Best regards,
Joan
P.S.: If you do not wish to receive any more announcements, please send an email to
bagaria@ub.edu with the text “Unsubscribe”.
Joan Bagaria
ICREA Research Professor
Universitat de Barcelona
Departament de Matemàtiques i Informàtica
Gran Via de les Corts Catalanes 585
08007 Barcelona
Catalonia
Phone: +34 93 402 1609
Joan Bagaria
ICREA Research Professor
Universitat de Barcelona
Departament de Matemàtiques i Informàtica
Gran Via de les Corts Catalanes 585
08007 Barcelona
Catalonia
Phone: +34 93 402 1609
joan.bagaria@icrea.catbagaria@ub.edu
Event Tuesday, September 21
Carnegie Mellon Logic Seminar
9/15/2021 21:07:08
TUESDAY, September 21, 2021
Set Theory Reading Group: 4:30 P.M., Online, Allison Wang, Carnegie
Mellon University
Zoom link:
https://cmu.zoom.us/j/621951121?pwd=eWEwVit5WUxlUExOWE51ajdFZnJ2Zz09
Meeting ID: 621 951 121
Passcode: 617076
TITLE: Hyperfiniteness and Ramsey notions of largeness
ABSTRACT: The lowest non-trivial complexity class in the theory of
Countable Borel Equivalence Relations (CBERs) is the class of hyperfinite
CBERs. One difficulty that arises in studying this class is determining
which CBERs are hyperfinite. Measure theory can be used to answer this
question, but not many techniques can. For instance, a Baire category
approach cannot distinguish hyperfinite CBERS: a result of Hjorth and
Kechris states that every CBER on a Polish space is hyperfinite when
restricted to some comeager set. We will discuss a classical proof of
Mathias's theorem that every CBER on the Ellentuck Ramsey space is
hyperfinite when restricted to some pure Ellentuck cube. Mathias's theorem
implies that a Ramsey-theoretic approach also cannot distinguish
hyperfinite CBERs.
This is joint work with Aristotelis Panagiotopoulos.
ORGANIZER'S NOTE: The talk will start after some socializing, at around
4:40 or 4:45.
Wednesday seminar
Prague Set Theory Seminar
9/14/2021 13:33:01
Dear all,
We will restart the Wednesday seminar again this autumn. Hopefully we
will not need pause it because of the pandemic again.
The seminar should meet at the usual time and place, starting on
Wednesday September 29.
Please let me know in case you would know any email addresses I should
add to the mailing list, or in case you would like to be removed from
the list.
The seminar meets on Wednesday September 29th at 11:00 in the Institute
of Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.
Program: Chris Lambie Hanson -- Strongly unbounded functions and
productivity of chain conditions
We discuss the existence of strongly unbounded functions on pairs of
ordinals, which provide strong counterexamples to generalizations of
Ramsey's theorem to uncountable cardinals. The talk will include a
brief, gentle introduction to Todorcevic's powerful technique of walks
on ordinals and an application to the infinite productivity of the
$\kappa$-Knaster property.
Some of the results are joint work with Assaf Rinot.
Best,
David
Logic Seminar Wed 15 Sept 2021 16:00 hrs at NUS by Bakhadyr Khoussainov
NUS Logic Seminar
9/12/2021 23:11:16
Invitation to the Logic Seminar at the National University of Singapore
Date: Wednesday, 15 September 2021, 16:00 hrs
Talk via Zoom:
https://nus-sg.zoom.us/j/83049258042?pwd=UWViaWNvTFUrdFdhOHJCdEVydnVkdz09
Meeting ID: 830 4925 8042
Passcode: 1729=x3+y3
Speaker: Bakhadyr Khoussainov, UESTC, Chengdu and The University of Auckland
Title: Probability Structures
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Abstract:
This talk belongs to the area of probabilistic logic semantics.
The first contribution of this work is the introduction of probability
structures. Probability structures are the algebraic structures
equipped with probability functions on the domains and the atomic
predicates. These structures extend type 1 probability structures
introduced by Halpern and Bacchus.
Type 1 probability structures contain probability functions on domains
only. Our probability structures possess an additional statistical
knowledge, - probability functions on atomic predicates.
We present a method that builds probability spaces for the first order
logic formulas and prove that our semantics is sound.
The second contribution of this work is the introduction of smooth
probability structures.
The smooth probability structures carefully refine probability
structures so that we have a better control of the probability spaces
defined by first order logic formulas. For these structures we
initiate the study of first order probability logic (FOPLS),
investigate axiomatizability of FOPLS, and address decidability and
undecidability questions of the sets of valid formulas. We also study
a few algorithmic questions on probability structures.
Logic Seminar Today 16:00 hrs SGT at NUS by Khoussainov and Stephan
NUS Logic Seminar
9/7/2021 21:44:37
Hello, the password of this reminder was wrong, here the amended version.
Invitation to the Logic Seminar at the National University of Singapore
Date: Wednesday, 8 September 2021, 16:00 hrs, Singapore Time Zone (GMT+8 hrs)
Talk via Zoom:
https://nus-sg.zoom.us/j/83049258042?pwd=UWViaWNvTFUrdFdhOHJCdEVydnVkdz09
Meeting ID: 830 4925 8042
Passcode: 1729=x3+y3
Speaker: Bakhadyr Khoussainov and Frank Stephan
Title: Parity Games - Background and Algorithms.
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Abstract:
Parity games are games where a marker is moved on a finite graph and each
node is annotated with a natural number; the game runs forever and the
largest number in an infinitely often visited node decides the winner,
if it is even then player Anke wins else player Boris wins. Marcin
Jurdzinski showed that this game is in UP intersected coUP and also
provided the first not fully exponential algorithm for it; however,
the exact time complexity remained unresolved.
In 2017, Calude, Jain, Khoussainov, Li and Stephan found a quasipolynomial
time algorithm which Jurdzinski and Lazic as well as Fearnley, Jain,
Schewe, Stephan and Wojtczak improved the algorithm to be in polynomial
space as well as quasipolynomial time.
The talk provides the way this algorithm was found and the implications
it has for the fixed-parameter-tracktability of parity games and related
problems like coloured Muller games. Though now quite a number of
quasipolynomial time algorithms are known and there is quite extensive
research in this topic, the question on whether parity games can even
be solved in polynomial time is still unresolved.
This talk is given by Bakhadyr Khoussainov and Frank Stephan jointly
also on behalf of their coauthors Cristian Calude, Sanjay Jain and Wei Li.
Logic Seminar Today 16:00 hrs SGT at NUS by Khoussainov and Stephan
NUS Logic Seminar
9/7/2021 21:20:42
Invitation to the Logic Seminar at the National University of Singapore
Date: Wednesday, 8 September 2021, 16:00 hrs, Singapore Time Zone (GMT+8 hrs)
Talk via Zoom:
https://nus-sg.zoom.us/j/83049258042?pwd=3DUWViaWNvTFUrdFdhOHJCdEVydnVkdz09
Meeting ID: 830 4925 8042
Passcode: 1729=3Dx3+y3
Speaker: Bakhadyr Khoussainov and Frank Stephan
Title: Parity Games - Background and Algorithms.
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Abstract:
Parity games are games where a marker is moved on a finite graph and each
node is annotated with a natural number; the game runs forever and the
largest number in an infinitely often visited node decides the winner,
if it is even then player Anke wins else player Boris wins. Marcin
Jurdzinski showed that this game is in UP intersected coUP and also
provided the first not fully exponential algorithm for it; however,
the exact time complexity remained unresolved.
In 2017, Calude, Jain, Khoussainov, Li and Stephan found a quasipolynomial
time algorithm which Jurdzinski and Lazic as well as Fearnley, Jain,
Schewe, Stephan and Wojtczak improved the algorithm to be in polynomial
space as well as quasipolynomial time.
The talk provides the way this algorithm was found and the implications
it has for the fixed-parameter-tracktability of parity games and related
problems like coloured Muller games. Though now quite a number of
quasipolynomial time algorithms are known and there is quite extensive
research in this topic, the question on whether parity games can even
be solved in polynomial time is still unresolved.
This talk is given by Bakhadyr Khoussainov and Frank Stephan jointly
also on behalf of their coauthors Cristian Calude, Sanjay Jain and Wei Li.
Logic Seminar 8 September 2021 16:00 hrs at NUS by Bakhadyr Khoussainov and Frank Stephan
NUS Logic Seminar
9/2/2021 20:42:56
Hello, there is a typing error in the below email.
It should be "8 September 2021", so Wednesday next week. Frank Stephan
On Thu, Sep 02, 2021 at 11:18:49PM +0800, Frank STEPHAN wrote:
> Invitation to the Logic Seminar at the National University of Singapore
>
> Date: Wednesday, CORRECTED TO 08 Sep 2021, 16:00 hrs
>
> Talk via Zoom:
> https://nus-sg.zoom.us/j/83049258042?pwd=UWViaWNvTFUrdFdhOHJCdEVydnVkdz09
> Meeting ID: 830 4925 8042
> Passcode: 1729=x3+y3
>
> Speaker: Bakhadyr Khoussainov and Frank Stephan
>
> Title: Parity Games - Background and Algorithms.
>
> URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
>
> Abstract:
> Parity games are games where a marker is moved on
> a finite graph and each node is annotated with a
> natural number; the game runs forever and the largest
> number in an infinitely often visited node decides
> the winner, if it is even then player Anke wins
> else player Boris wins. Marcin Jurdzinski showed
> that this game is in UP intersected coUP and also
> provided the first not fully exponential algorithm
> for it; however, the exact time complexity remained
> unresolved. In 2017, Calude, Jain, Khoussainov, Li
> and Stephan found a quasipolynomial time algorithm
> which Jurdzinski and Lazic as well as Schewe and his
> collaborators improved to be in polynomial space
> as well. The talk provides the way this algorithm
> was found and the implications it has for the
> fixed-parameter-tracktability of parity games and
> related problems like coloured Muller games. Though
> now quite a number of quasipolynomial time algorithms
> are known and there is quite extensive research in this
> topic, the question on whether parity games can even
> be solved in polynomial time is still unresolved.
>
> This talk is given by Bakhadyr Khoussainov and
> Frank Stephan jointly also on behalf of their coauthors
> Cristian Calude, Sanjay Jain and Wei Li.
>
Logic Seminar 8 September 2021 16:00 hrs at NUS by Bakhadyr Khoussainov and Frank Stephan
NUS Logic Seminar
9/2/2021 11:18:49
Invitation to the Logic Seminar at the National University of Singapore
Date: Wednesday, 11 August 2021, 16:00 hrs
Talk via Zoom:
https://nus-sg.zoom.us/j/83049258042?pwd=UWViaWNvTFUrdFdhOHJCdEVydnVkdz09
Meeting ID: 830 4925 8042
Passcode: 1729=x3+y3
Speaker: Bakhadyr Khoussainov and Frank Stephan
Title: Parity Games - Background and Algorithms.
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Abstract:
Parity games are games where a marker is moved on
a finite graph and each node is annotated with a
natural number; the game runs forever and the largest
number in an infinitely often visited node decides
the winner, if it is even then player Anke wins
else player Boris wins. Marcin Jurdzinski showed
that this game is in UP intersected coUP and also
provided the first not fully exponential algorithm
for it; however, the exact time complexity remained
unresolved. In 2017, Calude, Jain, Khoussainov, Li
and Stephan found a quasipolynomial time algorithm
which Jurdzinski and Lazic as well as Schewe and his
collaborators improved to be in polynomial space
as well. The talk provides the way this algorithm
was found and the implications it has for the
fixed-parameter-tracktability of parity games and
related problems like coloured Muller games. Though
now quite a number of quasipolynomial time algorithms
are known and there is quite extensive research in this
topic, the question on whether parity games can even
be solved in polynomial time is still unresolved.
This talk is given by Bakhadyr Khoussainov and
Frank Stephan jointly also on behalf of their coauthors
Cristian Calude, Sanjay Jain and Wei Li.
Logic Seminar today 16:00 hrs at NUS by Rupert Hoelzl, University of the Bundeswehr in Munich
NUS Logic Seminar
9/1/2021 3:33:32
Invitation to the Logic Seminar at the National University of Singapore
Date: Wednesday, 1 September 2021, 16:00 hrs
Talk via Zoom:
https://nus-sg.zoom.us/j/83049258042?pwd=UWViaWNvTFUrdFdhOHJCdEVydnVkdz09
Meeting ID: 830 4925 8042
Passcode: 1729=x3+y3
Speaker: Rupert Hoelzl
Title: The reverse mathematics of inductive inference
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Abstract:
We investigates inductive inference from the perspective
of reverse mathematics. Reverse mathematics is a framework that
allows gauging the proof strength of theorems and axioms in many
areas of mathematics. We apply its methods to
basic notions of algorithmic learning theory such as Angluin's tell-tale
criterion and its variants for learning in the limit and for
conservative learning, as well as to the
more general scenario of partial learning.
These notions are studied in the reverse mathematics context
for uniformly and weakly represented families of languages. The results
are stated in terms of axioms referring to induction strength and to
domination of weakly represented families of functions.
Free Registration for IPEC 2021 until 29 August 2021 (Online Conference)
NUS Logic Seminar
8/28/2021 1:38:56
Hello,
Most likely on 8 September 2021, Bakhadyr Khoussainov and Frank Stephan
will give an invited talk about the paper
Deciding parity games in quasipolynomial time
by Cristian Calude, Sanjay Jain, Bakhadyr Khoussainov,
Wei Li and Frank Stephan
from STOC 2017 and SIAM Journal on Computing
at IPEC 2021. You can up to tomorrow (29 August 2021) register for free
at this online occurring conference through the webpage
http://algo2021.tecnico.ulisboa.pt/index.html#registration
and information on the conference IPEC is on
http://algo2021.tecnico.ulisboa.pt/IPEC2021/index.html
The exact programme is not yet there, but will most likely be made available
after tomorrow's free registration deadline for nonpresenting participants.
IPEC is an International Symposium on Parameterised and Exact Computation.
Sorry for the short notice, I was waiting for info about the conference
going onto the webpage before sending this.
Best regards, Frank
Felix Weilacher on Tuesday (8/31) 3:30 PM Eastern
Carnegie Mellon Logic Seminar
8/27/2021 12:18:31
TUESDAY, August 31 2021
Mathematical logic seminar: 3:30 P.M., Online, Felix Weilacher, Carnegie
Mellon University
Zoom link:
https://cmu.zoom.us/j/621951121?pwd=eWEwVit5WUxlUExOWE51ajdFZnJ2Zz09
Meeting ID: 621 951 121
Passcode: 617076
TITLE: Borel Edge Colorings for Finite Dimensional Groups
ABSTRACT: In Borel graph combinatorics, one often produces a structure
(e.g. a coloring) by dividing a graph into subgraphs with finite connected
components, then defining the structure on those components via some
straightforward uniformization result. We first give an overview of some
recent work formalizing these notions and applying them to various
problems. We then present our own application to the problem of edge
coloring. For Borel actions of certain groups, we find "degree plus one"
Borel edge colorings, matching the classical bound of Vizing. Furthermore,
for finitely generated abelian groups, we are able to exactly determine
Borel edge chromatic numbers.
Logic Seminar 1 Sept 2021 16:00 hrs at NUS by Rupert Hoelzl, Univ. of the Bundeswehr, Munich
NUS Logic Seminar
8/27/2021 10:50:00
Invitation to the Logic Seminar at the National University of Singapore
Date: Wednesday, 1 September 2021, 16:00 hrs
Talk via Zoom:
https://nus-sg.zoom.us/j/83049258042?pwd=UWViaWNvTFUrdFdhOHJCdEVydnVkdz09
Meeting ID: 830 4925 8042
Passcode: 1729=x3+y3
Speaker: Rupert Hoelzl
Title: The reverse mathematics of inductive inference
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
We investigates inductive inference from the perspective
of reverse mathematics. Reverse mathematics is a framework that
allows gauging the proof strength of theorems and axioms in many
areas of mathematics. We apply its methods to basic notions of algorithmic
learning theory such as Angluin's tell-tale criterion and its variants
for learning in the limit and for conservative learning, as well as to the
more general scenario of partial learning.
These notions are studied in the reverse mathematics context
for uniformly and weakly represented families of languages. The results
are stated in terms of axioms referring to induction strength and to
domination of weakly represented families of functions.
Logic Seminar 25 April 2021 16:00 hrs by Ng Keng Meng (NTU) at NUS (today)
NUS Logic Seminar
8/25/2021 1:41:23
Invitation to the Logic Seminar at the National University of Singapore
Date: Wednesday, 25 August 2021, 16:00 hrs
Talk via Zoom:
https://nus-sg.zoom.us/j/83049258042?pwd=UWViaWNvTFUrdFdhOHJCdEVydnVkdz09
Meeting ID: 830 4925 8042
Passcode: 1729=x3+y3
Speaker: Ng Keng Meng
Title: Are the rationals dense
Abstract:
There has been a recent revival in the interest in sub-computable
mathematics. One of these approaches is to consider ``primitive
recursive'' or punctual structures. This has led to a greater
understanding in the effective content of well-known objects and
proofs in classical computability theory. When considering the
punctual anaologies of classical computabilitiy we often obtain
strange and surprising results. I will discuss some recent work in
progress in this area, focussing particularly on structural results.
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
RIMS Set Theory Workshop: October 12-15, 2021
Conference
8/23/2021
RIMS SET THEORY WORKSHOP 2021
Announcement / Call for Contributions
RIMS workshop "Recent Developments in Set Theory of the Reals"
Date: Tuesday, October 12, 2021 to Friday, October 15, 2021
Venue: ONLINE (via ZOOM meeting), based on Japan Standard Time 9am--5pm
Contact: Masaru Kada (Osaka Prefecture University) / kada@mi.s.osakafu-u.ac.jp
Workshop Overview:
This online workshop, hosted by RIMS (Research Institute for Mathematical Sciences, Kyoto University), is mainly (but not only) focused on recent developments in set theory of the reals. The program will contain a minicourse (a series of lectures) as well as contributed talks. In the minicourse, we invite Joerg Brendle (Kobe University) and Diego Mejia (Shizuoka University), who will give us lectures on some forcing techniques (e.g., Boolean ultrapowers, submodel methods, etc.) and related results in set theory of the reals.
We welcome every researcher in set theory or related research fields. Please join us!
Registration:
Please submit a registration form to register your participation / contributed talk, from the following URL:
https://forms.gle/1156YFMp1bN9GEDJ9
Deadline for contributed talks: September 9, 2021
Deadline for participation: October 10, 2021
Tagged: Joerg Brendle, Diego Mejia
First math logic seminar of the new semester
Carnegie Mellon Logic Seminar
8/16/2021 9:25:09
TUESDAY, August 31 2021
Mathematical logic seminar: 3:30 P.M., Online, Felix Weilacher, Carnegie
Mellon University
Zoom link:
https://cmu.zoom.us/j/621951121?pwd=eWEwVit5WUxlUExOWE51ajdFZnJ2Zz09
Meeting ID: 621 951 121
Passcode: 617076
TITLE: Borel Edge Colorings for Finite Dimensional Groups
ABSTRACT: In Borel graph combinatorics, one often produces a structure
(e.g. a coloring) by dividing a graph into subgraphs with finite connected
components, then defining the structure on those components via some
straightforward uniformization result. We first give an overview of some
recent work formalizing these notions and applying them to various
problems. We then present our own application to the problem of edge
coloring. For Borel actions of certain groups, we find "degree plus one"
Borel edge colorings, matching the classical bound of Vizing. Furthermore,
for finitely generated abelian groups, we are able to exactly determine
Borel edge chromatic numbers.
Logic Seminar at NUS on Wed 18 Aug 2021 at 16:00 hrs
NUS Logic Seminar
8/15/2021 23:15:55
Invitation to the Logic Seminar at the National University of Singapore
Date: Wednesday, 18 August 2021, 16:00 hrs
Talk via Zoom:
https://nus-sg.zoom.us/j/83049258042?pwd=UWViaWNvTFUrdFdhOHJCdEVydnVkdz09
Meeting ID: 830 4925 8042
Passcode: 1729=x3+y3
Speaker: Yu Liang, Nanjing University
Title: Generalizing Besicovitch-Davis theorem
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Besicovitch-Davis theorem says that the Hausdorff dimension of
every analytic set can be approximated by its closed subset. But the
Besicovitch-Davis theorem fails for co-analytic sets under the assumption
V=L as observed by Slaman. We prove that the theorem holds for arbitrary
sets under ZF+sTD. We also prove that the theorem holds for
Sigma-1-2-sets under Martin's axiom.
This is joint work with Peng Yinhe and Wu Liuzhen.
Logic Seminar 11 Aug 2021 16:00 hrs at NUS by Frank Stephan
NUS Logic Seminar
8/7/2021 10:53:30
Invitation to the Logic Seminar at the National University of Singapore
Date: Wednesday, 11 August 2021, 16:00 hrs
Talk via Zoom:
https://nus-sg.zoom.us/j/83049258042?pwd=UWViaWNvTFUrdFdhOHJCdEVydnVkdz09
Meeting ID: 830 4925 8042
Passcode: 1729=x3+y3
Speaker: Frank Stephan
Title: A survey on the structures realised by positive equivalence relations
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Abstract:
Let a positive equivalence relation to be an r.e. equivalence
relation on the set of natural numbers with infinitely many
equivalence relations. Khoussainov initiated with coauthors
a deep study of the following question: Given a positive equivalence
relation eta, which structures from a given set of structures does
this equivalence relation realise? Here realisation means that
functions in the structure are recursive and relations are r.e.
with the equality itself given by the equivalence relation eta.
In other words, the given r.e. structure divided by eta is the
structure realised by eta. Now questions studied by Khoussainov
and his coworkers included questions like "What is the partial
ordering on positive equivalence relations eta,rho where
eta is below rho iff every structure of the given type realised by eta
is also realised by rho?
Besides algebraic structures and orders, it has also been studied
how the learnability notions behave with respect to uniformly
r.e. one-one families realised by positive equivalence relations.
Events next Tuesday
Carnegie Mellon Logic Seminar
8/6/2021 12:23:57
TUESDAY, August 10 2021
Mathematical logic seminar: 3:30 P.M., Online, Nathaniel Bannister,
Carnegie Mellon University (beginning Fall, 2021)
Zoom link:
https://cmu.zoom.us/j/621951121?pwd=eWEwVit5WUxlUExOWE51ajdFZnJ2Zz09
Meeting ID: 621 951 121
Passcode: 617076
TITLE: Additivity of strong homology for locally compact separable metric
spaces (part 6)
ABSTRACT: This series of talks will cover the 2019 paper "On the
additivity of strong homology for locally compact separable metric spaces"
as well as recent work establishing a conceptual basis for the results
therein. We will show that (relative to a weakly compact cardinal) it is
consistent for strong homology to be additive and compactly supported on
the class of locally compact separable metric spaces. In the process, we
develop an equivalent algebraic statement and a sufficient
cardinal-theoretic condition.
This is joint work with Justin Moore, Jeffrey Bergfalk, and Stevo
Todorcevic.
TUESDAY, August 10, 2021
Set Theory Reading Group: 4:30 P.M., Online, Nathaniel Bannister,
Carnegie Mellon University (beginning Fall, 2021)
Zoom link:
https://cmu.zoom.us/j/621951121?pwd=eWEwVit5WUxlUExOWE51ajdFZnJ2Zz09
Meeting ID: 621 951 121
Passcode: 617076
TITLE: Additivity of strong homology for locally compact separable metric
spaces (part 7)
ABSTRACT: This series of talks will cover the 2019 paper "On the
additivity of strong homology for locally compact separable metric spaces"
as well as recent work establishing a conceptual basis for the results
therein. We will show that (relative to a weakly compact cardinal) it is
consistent for strong homology to be additive and compactly supported on
the class of locally compact separable metric spaces. In the process, we
develop an equivalent algebraic statement and a sufficient
cardinal-theoretic condition.
This is joint work with Justin Moore, Jeffrey Bergfalk, and Stevo
Todorcevic.
Events next Tuesday
Carnegie Mellon Logic Seminar
7/29/2021 12:09:24
ORGANIZER'S NOTE: Video recordings of Nathaniel Bannister's seminar series
are being made available online. Please email me for details if you would
like access.
TUESDAY, August 3, 2021
Mathematical logic seminar: 3:30 P.M., Online, Nathaniel Bannister,
Carnegie Mellon University (beginning Fall, 2021)
Zoom link:
https://cmu.zoom.us/j/621951121?pwd=eWEwVit5WUxlUExOWE51ajdFZnJ2Zz09
Meeting ID: 621 951 121
Passcode: 617076
TITLE: Additivity of strong homology for locally compact separable metric
spaces (part 4)
ABSTRACT: This series of talks will cover the 2019 paper "On the
additivity of strong homology for locally compact separable metric spaces"
as well as recent work establishing a conceptual basis for the results
therein. We will show that (relative to a weakly compact cardinal) it is
consistent for strong homology to be additive and compactly supported on
the class of locally compact separable metric spaces. In the process, we
develop an equivalent algebraic statement and a sufficient
cardinal-theoretic condition.
This is joint work with Justin Moore, Jeffrey Bergfalk, and Stevo
Todorcevic.
TUESDAY, August 3, 2021
Set Theory Reading Group: 4:30 P.M., Online, Nathaniel Bannister,
Carnegie Mellon University (beginning Fall, 2021)
Zoom link:
https://cmu.zoom.us/j/621951121?pwd=eWEwVit5WUxlUExOWE51ajdFZnJ2Zz09
Meeting ID: 621 951 121
Passcode: 617076
TITLE: Additivity of strong homology for locally compact separable metric
spaces (part 5)
ABSTRACT: This series of talks will cover the 2019 paper "On the
additivity of strong homology for locally compact separable metric spaces"
as well as recent work establishing a conceptual basis for the results
therein. We will show that (relative to a weakly compact cardinal) it is
consistent for strong homology to be additive and compactly supported on
the class of locally compact separable metric spaces. In the process, we
develop an equivalent algebraic statement and a sufficient
cardinal-theoretic condition.
This is joint work with Justin Moore, Jeffrey Bergfalk, and Stevo
Todorcevic.
Logic seminar and set theory reading group for next week
Carnegie Mellon Logic Seminar
7/24/2021 11:04:29
ORGANIZERS' NOTE: Last week, these seminars were postponed until next week
due to last minute technical issues.
--------------------------------------------------------------------------
TUESDAY, July 27, 2021
Mathematical logic seminar: 3:30 P.M., Online, Nathaniel Bannister, Carnegie
Mellon University (beginning Fall, 2021)
Zoom link:
https://cmu.zoom.us/j/621951121?pwd=eWEwVit5WUxlUExOWE51ajdFZnJ2Zz09
Meeting ID: 621 951 121
Passcode: 617076
TITLE: Additivity of strong homology for locally compact separable metric
spaces (part 2)
ABSTRACT: This series of talks will cover the 2019 paper "On the additivity of
strong homology for locally compact separable metric spaces" as well
as recent work establishing a conceptual basis for the results therein. We
will show that (relative to a weakly compact cardinal) it is consistent
for strong homology to be additive and compactly supported on the class of
locally compact separable metric spaces. In the process, we develop an
equivalent algebraic statement and a sufficient cardinal-theoretic condition.
This is joint work with Justin Moore, Jeffrey Bergfalk, and Stevo Todorcevic.
TUESDAY, July 27, 2021
Set Theory Reading Group: 4:30 P.M., Online, Nathaniel Bannister, Carnegie
Mellon University (beginning Fall, 2021)
Zoom link:
https://cmu.zoom.us/j/621951121?pwd=eWEwVit5WUxlUExOWE51ajdFZnJ2Zz09
Meeting ID: 621 951 121
Passcode: 617076
TITLE: Additivity of strong homology for locally compact separable metric
spaces (part 3)
ABSTRACT: This series of talks will cover the 2019 paper "On the additivity
of strong homology for locally compact separable metric spaces" as well
as recent work establishing a conceptual basis for the results therein. We
will show that (relative to a weakly compact cardinal) it is consistent
for strong homology to be additive and compactly supported on the class of
locally compact separable metric spaces. In the process, we develop an
equivalent algebraic statement and a sufficient cardinal-theoretic condition.
This is joint work with Justin Moore, Jeffrey Bergfalk, and Stevo Todorcevic.
An apology to all about today's seminar
Toronto Set Theory Seminar
7/23/2021 16:26:09
Hello everyone,
As some of you noticed, today there was no seminar although it was announced and not cancelled. We are very sorry about this miscommunication on our end.
Also, I offer an apology to everyone for not being in the meeting to explain the situation.
Last minute yesterday, we found out that the speaker was not going to be able to assist. I was supposed to send an email cancelling the seminar today, but I didn't.
Today I got my first vaccine shot so my mind was elsewhere (along with my internet and my computer), so I was not able to warn everyone about the cancellation.
Again, we offer an apology. This speaker will be able to participate in the seminar in september. In the meanwhile, we do not have seminar next week.
I thank everyone for your comprehension.
Best regards
Iván Ongay Valverde (he/his)
Talk tomorrow by Gianluca Paolini at 1 30 pm (Toronto time)
Toronto Set Theory Seminar
7/22/2021 13:30:00
Hello everyone,
Please use the
following link and, only in case that it appears, fill the form (every
week) to enter the meeting. This form helps the Field Institute to know
statistical data about attendance.
Here the speaker information:
Speaker:Gianluca Paolini
Date and Time: Friday, July 23rd, 2021 - 1:30pm to 3:00pm
Title: Torsion-Free Abelian Groups are Borel Complete
Abstract:
We prove that the Borel space of torsion-free Abelian groups with domain ω
is Borel complete, i.e., the isomorphism relation on this Borel space
is as complicated as possible, as an isomorphism relation. This solves a
long-standing open problem in descriptive set theory, which dates back
to the seminal paper on Borel reducibility of Friedman and Stanley from
1989.
Iván Ongay Valverde (he/his)
Talk Friday 23rd June by Gianluca Paolini at 1 30 pm (Toronto time)
Toronto Set Theory Seminar
7/17/2021 13:30:00
Hello everyone,
Please use the
following link and, only in case that it appears, fill the form (every
week) to enter the meeting. This form helps the Field Institute to know
statistical data about attendance.
Here the speaker information:
Speaker:Gianluca Paolini
Date and Time: Friday, July 23rd, 2021 - 1:30pm to 3:00pm
Title: Torsion-Free Abelian Groups are Borel Complete
Abstract:
We prove that the Borel space of torsion-free Abelian groups with domain ω
is Borel complete, i.e., the isomorphism relation on this Borel space
is as complicated as possible, as an isomorphism relation. This solves a
long-standing open problem in descriptive set theory, which dates back
to the seminal paper on Borel reducibility of Friedman and Stanley from
1989.
Iván Ongay Valverde (he/his)
Talk in ONE hour by Richard Matthews
Toronto Set Theory Seminar
7/16/2021 12:30:00
Hello everyone,
Please use the
following link and, only in case that it appears, fill the form (every
week) to enter the meeting. This form helps the Field Institute to know
statistical data about attendance.
Here the speaker information:
Speaker: Richard Matthews
Date and Time: Friday, July 16th, 2021 - 1:30pm to 3:00pm
Title: Large Cardinals in Weakened Axiomatic Theories
Abstract:
The
Kunen Inconsistency is an important milestone in the study of axiomatic
set theory, placing a hard limit on how close the target model of a
non-trivial elementary embedding can be to the full universe. In
particular, it shows that the existence of a Reinhardt embedding, that
is a non-trivial embedding of the full universe into itself, is
inconsistent. It is well-known that all proofs we currently have rely
extensively on the fact that we are working with the full power of ZFC,
most notably the essential use of choice.
In this talk we shall discuss the notion of a Reinhardt embedding
over several weakened base theories, primarily ZFC without Power Set,
Zermelo and Power Kripke Platek. We shall see how to obtain some upper
bounds, lower bounds and equiconsistency results in terms of the usual
ZFC large cardinal hierarchy as well as many unexpected characteristics
such embeddings can have. Moreover, we shall see that, under reasonable
additional assumptions, it is possible to reobtain Kunen-type
inconsistency results in both ZFC without Power Set and Power Kripke
Platek plus Well-Ordering.
Iván Ongay Valverde (he/his)
Events next Tuesday
Carnegie Mellon Logic Seminar
7/16/2021 12:15:05
TUESDAY, July 20, 2021
Mathematical logic seminar: 3:30 P.M., Online, Nathaniel Bannister,
Carnegie Mellon University (beginning Fall, 2021)
Join Zoom Meeting: https://cmu.zoom.us/j/621951121 [cmu.zoom.us]
Meeting ID: 621 951 121
TITLE: Additivity of strong homology for locally compact separable metric
spaces (part 2)
ABSTRACT: This series of talks will cover the 2019 paper "On the
additivity of strong homology for locally compact separable metric spaces"
as well as recent work establishing a conceptual basis for the results
therein. We will show that (relative to a weakly compact cardinal) it is
consistent for strong homology to be additive and compactly supported on
the class of locally compact separable metric spaces. In the process, we
develop an equivalent algebraic statement and a sufficient
cardinal-theoretic condition.
This is joint work with Justin Moore, Jeffrey Bergfalk, and Stevo
Todorcevic.
TUESDAY, July 20, 2021
Set Theory Reading Group: 4:30 P.M., Online, Nathaniel Bannister,
Carnegie Mellon University (beginning Fall, 2021)
Join Zoom Meeting: https://cmu.zoom.us/j/621951121 [cmu.zoom.us]
Meeting ID: 621 951 121
TITLE: Additivity of strong homology for locally compact separable metric
spaces (part 3)
ABSTRACT: This series of talks will cover the 2019 paper "On the
additivity of strong homology for locally compact separable metric spaces"
as well as recent work establishing a conceptual basis for the results
therein. We will show that (relative to a weakly compact cardinal) it is
consistent for strong homology to be additive and compactly supported on
the class of locally compact separable metric spaces. In the process, we
develop an equivalent algebraic statement and a sufficient
cardinal-theoretic condition.
This is joint work with Justin Moore, Jeffrey Bergfalk, and Stevo
Todorcevic.
Today at 1 30 pm talk by Richard Matthews (Toronto time)
Toronto Set Theory Seminar
7/16/2021 7:45:00
Hello everyone,
Please use the
following link and, only in case that it appears, fill the form (every
week) to enter the meeting. This form helps the Field Institute to know
statistical data about attendance.
Here the speaker information:
Speaker: Richard Matthews
Date and Time: Friday, July 16th, 2021 - 1:30pm to 3:00pm
Title: Large Cardinals in Weakened Axiomatic Theories
Abstract:
The
Kunen Inconsistency is an important milestone in the study of axiomatic
set theory, placing a hard limit on how close the target model of a
non-trivial elementary embedding can be to the full universe. In
particular, it shows that the existence of a Reinhardt embedding, that
is a non-trivial embedding of the full universe into itself, is
inconsistent. It is well-known that all proofs we currently have rely
extensively on the fact that we are working with the full power of ZFC,
most notably the essential use of choice.
In this talk we shall discuss the notion of a Reinhardt embedding
over several weakened base theories, primarily ZFC without Power Set,
Zermelo and Power Kripke Platek. We shall see how to obtain some upper
bounds, lower bounds and equiconsistency results in terms of the usual
ZFC large cardinal hierarchy as well as many unexpected characteristics
such embeddings can have. Moreover, we shall see that, under reasonable
additional assumptions, it is possible to reobtain Kunen-type
inconsistency results in both ZFC without Power Set and Power Kripke
Platek plus Well-Ordering.
Iván Ongay Valverde (he/his)
Two events on Tuesday
Carnegie Mellon Logic Seminar
7/11/2021 20:52:46
TUESDAY, July 13, 2021
Mathematical logic seminar: 3:30 P.M., Online, Nathaniel Bannister,
Carnegie Mellon University (beginning Fall, 2021)
Join Zoom Meeting: https://cmu.zoom.us/j/621951121 [cmu.zoom.us]
Meeting ID: 621 951 121
TITLE: An introduction to strong homology
ABSTRACT: We will introduce strong homology, which aims to correct the
failures of Čech homology, particularly the failure of exactness.
TUESDAY, July 13, 2021
Set Theory Reading Group: 4:30 P.M., Online, Nathaniel Bannister,
Carnegie Mellon University (beginning Fall, 2021)
Join Zoom Meeting: https://cmu.zoom.us/j/621951121 [cmu.zoom.us]
Meeting ID: 621 951 121
TITLE: Additivity of strong homology for locally compact separable metric
spaces (part 1)
ABSTRACT: This series of talks will cover the 2019 paper "On the
additivity of strong homology for locally compact separable metric spaces"
as well as recent work establishing a conceptual basis for the results
therein. We will show that (relative to a weakly compact cardinal) it is
consistent for strong homology to be additive and compactly supported on
the class of locally compact separable metric spaces. In the process, we
develop an equivalent algebraic statement and a sufficient
cardinal-theoretic condition. This is joint work with Justin Moore,
Jeffrey Bergfalk, and Stevo Todorcevic.
Talk Tomorrow by Osvaldo Guzmán 1 30 pm (Totonto time)
Toronto Set Theory Seminar
7/8/2021 10:25:00
Hello everyone,
Please use the following link and, only in case that it appears, fill the form (every week) to enter the meeting. This form helps the Field Institute to know statistical data about attendance. See attached image or follow the link below.
Here the speaker information:
Speaker: Osvaldo Guzmán González
Date and Time: Friday, July 9th, 2021 - 1:30pm to 3:00pm
Title: MAD families and strategically bounding forcings
Abstract:
The notion of strategically bounding forcings is a natural game-theoretic
strengthening of the bounding property for partial orders. In this talk, we
will study the basic properties of strategically bounding forcings and talk
about indestructibility of MAD families. The motivation for this work is the
problem of Roitman. I will talk about results that were obtained with
Michael Hrusak, Joerg Brendle and Dilip Raghavan.
Iván Ongay Valverde (he/his)
Series finale
Carnegie Mellon Logic Seminar
7/5/2021 12:01:15
TUESDAY, July 6, 2021
Mathematical logic seminar: 3:30 P.M., Online, James Cummings, Carnegie
Mellon University
Join Zoom Meeting: https://cmu.zoom.us/j/621951121 [cmu.zoom.us]
Meeting ID: 621 951 121
TITLE: Homological algebra for logicians
ABSTRACT: This is part 7 of a short series of talks aimed at giving some
background for Nathaniel Bannister's forthcoming seminars. Nathaniel's
talks will describe his work with Bergfalk and Moore on the additivity of
strong homology.
I will give a rapid overview of some necessary background in homological
algebra (eg abelian categories, chain complexes, derived functors). I will
assume very little background, just familiarity with basic notions in
category theory (category, functor, natural transformation) and algebra
(the definition of an R-module).
TUESDAY, July 6, 2021
Set Theory Reading Group: 4:30 P.M., Online, James Cummings, Carnegie
Mellon University
Join Zoom Meeting: https://cmu.zoom.us/j/621951121 [cmu.zoom.us]
Meeting ID: 621 951 121
TITLE: Homological algebra for logicians
ABSTRACT: This is part 8 of a short series of talks aimed at giving some
background for Nathaniel Bannister's forthcoming seminars. Nathaniel's
talks will describe his work with Bergfalk and Moore on the additivity of
strong homology.
I will give a rapid overview of some necessary background in homological
algebra (eg abelian categories, chain complexes, derived functors). I will
assume very little background, just familiarity with basic notions in
category theory (category, functor, natural transformation) and algebra
(the definition of an R-module).
Talk this Friday (July 9th) by Osvaldo Guzmán 1 30 pm (Totonto time)
Toronto Set Theory Seminar
7/3/2021 21:25:44
Hello everyone,
Please use the following link and, only in case that it appears, fill the form (every week) to enter the meeting. This form helps the Field Institute to know statistical data about attendance.
TBD
Here the speaker information:
Speaker: Osvaldo Guzmán González
Date and Time: Friday, July 9th, 2021 - 1:30pm to 3:00pm
Title: MAD families and strategically bounding forcings
Abstract:
The notion of strategically bounding forcings is a natural game-theoretic
strengthening of the bounding property for partial orders. In this talk, we
will study the basic properties of strategically bounding forcings and talk
about indestructibility of MAD families. The motivation for this work is the
problem of Roitman. I will talk about results that were obtained with
Michael Hrusak, Joerg Brendle and Dilip Raghavan.
Iván Ongay Valverde (he/his)
James Cummings series continues
Carnegie Mellon Logic Seminar
6/25/2021 20:45:44
TUESDAY, June 29, 2021
Mathematical logic seminar: 3:30 P.M., Online, James Cummings, Carnegie
Mellon University
Join Zoom Meeting: https://cmu.zoom.us/j/621951121 [cmu.zoom.us]
Meeting ID: 621 951 121
TITLE: Homological algebra for logicians
ABSTRACT: This is part 5 of a short series of talks aimed at giving some
background for Nathaniel Bannister's forthcoming seminars. Nathaniel's
talks will describe his work with Bergfalk and Moore on the additivity of
strong homology.
I will give a rapid overview of some necessary background in homological
algebra (eg abelian categories, chain complexes, derived functors). I will
assume very little background, just familiarity with basic notions in
category theory (category, functor, natural transformation) and algebra
(the definition of an R-module).
TUESDAY, June 29, 2021
Set Theory Reading Group: 4:30 P.M., Online, James Cummings, Carnegie
Mellon University
Join Zoom Meeting: https://cmu.zoom.us/j/621951121 [cmu.zoom.us]
Meeting ID: 621 951 121
TITLE: Homological algebra for logicians
ABSTRACT: This is part 6 of a short series of talks aimed at giving some
background for Nathaniel Bannister's forthcoming seminars. Nathaniel's
talks will describe his work with Bergfalk and Moore on the additivity of
strong homology.
I will give a rapid overview of some necessary background in homological
algebra (eg abelian categories, chain complexes, derived functors). I will
assume very little background, just familiarity with basic notions in
category theory (category, functor, natural transformation) and algebra
(the definition of an R-module).
Talk TODAY by Riley Thornton 1 30 pm (Toronto time)
Toronto Set Theory Seminar
6/25/2021 7:00:00
Hello everyone,
Please use the
following link and, only in case that it appears, fill the form (every
week) to enter the meeting. This form helps the Field Institute to know
statistical data about attendance.
Here the speaker information:
Speaker:
Riley Thornton
Date and Time: Friday, June 25th, 2021 - 1:30pm to 3:00pm
Title: Effectivization in Borel Combinatorics
Abstract:
In Borel combinatorics, we often want to know when a Borel graph (or
equivalence relation, quasi-order, etc) admits a Borel witness to some
combinatorial property, Φ. An effectivization theorem for Φ says that any (lightface) Δ11 graph with a Borel witness to Φ in fact has a Δ11
witness. This kind of effectivization gives a strong upper bound on the
projective complexity of the set of graphs where a definable witness
exists and suggests that such graphs might admit a nice structural
characterization. This talk will present a streamlined method for
proving effectivization theorems, give a number of applications, and
discuss some related dichotomy theorems.
Iván Ongay Valverde (he/his)
Talk this Friday 25th (in less than two days) by Riley Thornton 1 30 pm (Toronto time)
Toronto Set Theory Seminar
6/23/2021 20:48:31
Hello everyone,
Please use the
following link and, only in case that it appears, fill the form (every
week) to enter the meeting. This form helps the Field Institute to know
statistical data about attendance.
Here the speaker information:
Speaker:
Riley Thornton
Date and Time: Friday, June 25th, 2021 - 1:30pm to 3:00pm
Title: Effectivization in Borel Combinatorics
Abstract:
In Borel combinatorics, we often want to know when a Borel graph (or
equivalence relation, quasi-order, etc) admits a Borel witness to some
combinatorial property, Φ. An effectivization theorem for Φ says that any (lightface) Δ11 graph with a Borel witness to Φ in fact has a Δ11
witness. This kind of effectivization gives a strong upper bound on the
projective complexity of the set of graphs where a definable witness
exists and suggests that such graphs might admit a nice structural
characterization. This talk will present a streamlined method for
proving effectivization theorems, give a number of applications, and
discuss some related dichotomy theorems.
I'll send the next reminder in the morning of the day of the talk
Iván Ongay Valverde (he/his)
(KGRC) research seminar talk on Thursday, June 24
Kurt Godel Research Center
6/21/2021 10:53:14
Research seminar
Kurt Gödel Research Center
Thursday, June 24
"Preserving levels of projective determinacy and regularity properties"
Johannes Schürz (TU Wien)
Since \mathbf{\Pi}^1_1-determinacy is a desirable property on the reals, the
natural question arises as to how one can preserve it under forcing. We will
show using the technique of capturing that the statement 'Every real has a
sharp' is preserved under any countable support iteration of 'simply' definable
forcing notions. By the famous results of L. Harrington and D. Martin this
shows that \mathbf{\Pi}^1_1-determinacy is preserved under such iterations.
More generally, our theorem also shows that the statement 'M_n^\sharp(x) exists
for every real x \in \omega^\omega' is preserved. By the results of I. Neeman
and H. Woodin this generalizes our result to higher levels of projective
determinacy.
Without the existence of large cardinals the technique of capturing can still
be used to show preservation results for regularity properties such as the
\mathbf{\Delta}^1_2- or \mathbf{\Sigma}^1_2-Baire property.
This is a joint project with J. Schilhan and P. Schlicht.
Time and Place
Talk at 3:00pm via Zoom: This talk will be given via Zoom. If you have not
received the meeting link by the day before the talk, please contact
richard.springer@univie.ac.at!
Talk tomorrow 18th by David Schrittesser (1:30 pm to 3pm Toronto time)
Toronto Set Theory Seminar
6/17/2021 8:00:00
Hello everyone,
Please use the
following link and, only in case that it appears, fill the form (every
week) to enter the meeting. This form helps the Field Institute to know
statistical data about attendance.
Here the speaker information:
Speaker:
David Schrittesser
Date and Time: Friday, June 18th, 2021 - 1:30pm to 3:00pm
Title:
A taste of nonstandard analysis and statistical decision theory
Abstract:
Statistical decision theory takes inspiration from game theory to
provide a basic framework in which one can reason about optimality (or
lack thereof) of statistical methods, such as estimators and tests.
One (very weak) property of such methods is admissibility - roughly, a
method of estimation is admissible if there is no other which does
better under all circumstances (in a sense specified by the decision
theoretical framework).
Although a weak property, admissibility is notoriously hard to
characterize. Recently we have found a characterization of admissibility
(in a large class of statistical problems) in Bayesian terms, by using
prior probability distributions which can take on infinitesimal values.
(The talk will not presuppose any knowledge on statistics or nonstandard
analysis. Joint work with D. Roy and H. Duanmu.)
Iván Ongay Valverde (he/his)
Talk this Friday 18th by David Schrittesser (1:30 pm to 3pm Toronto time)
Toronto Set Theory Seminar
6/16/2021 0:50:27
Hello everyone,
Please use the
following link and, only in case that it appears, fill the form (every
week) to enter the meeting. This form helps the Field Institute to know
statistical data about attendance.
Here the speaker information:
Speaker:
David Schrittesser
Date and Time: Friday, June 18th, 2021 - 1:30pm to 3:00pm
Title:
A taste of nonstandard analysis and statistical decision theory
Abstract:
Statistical decision theory takes inspiration from game theory to
provide a basic framework in which one can reason about optimality (or
lack thereof) of statistical methods, such as estimators and tests.
One (very weak) property of such methods is admissibility - roughly, a
method of estimation is admissible if there is no other which does
better under all circumstances (in a sense specified by the decision
theoretical framework).
Although a weak property, admissibility is notoriously hard to
characterize. Recently we have found a characterization of admissibility
(in a large class of statistical problems) in Bayesian terms, by using
prior probability distributions which can take on infinitesimal values.
(The talk will not presuppose any knowledge on statistics or nonstandard
analysis. Joint work with D. Roy and H. Duanmu.)
Iván Ongay Valverde (he/his)
(KGRC) research seminar talk and master defense Michael Zechner
Kurt Godel Research Center
6/14/2021 11:38:00
Research seminar
Kurt Gödel Research Center
Thursday, June 17
"Big Ramsey degrees of 3-uniform hypergraphs are finite"
David Chodounský
(Czech Academy of Sciences)
It is well known that the (universal countable) Rado graph has finite big
Ramsey degrees. I.e., given a finite colouring of n-tuples of its vertices
there is a copy of the Rado graph such that its n-tuples have at most
D(n)-many colours. The proof of this fact uses a theorem of Milliken for
trees, I will give sketch of the argument. I will moreover sketch an
extension of the proof which works also for universal structures with
higher arities, in particular 3-uniform hypergraphs.
Joint work with M. Balko, J. Hubička, M. Konečný, and L. Vena, see
https://arxiv.org/abs/2008.00268
Time and Place
Talk at 3:00pm via Zoom: This talk will be given via Zoom. If you have not
received the meeting link by the day before the talk, please contact
richard.springer@univie.ac.at!
* * *
Master defense
Friday, June 18
"Aspects of Vaught's Conjecture"
Michael Zechner
Examining committee:
Vera Fischer (Chair)
Sy Friedman (Thesis Supervisor)
Ben Miller (Reviewer)
Time and Place
Defense at 3:00pm via Moodle/BigBlueButton: This talk will be given via
Moodle/BigBlueButton. If you have not received the guest link by the day
before the talk, please contact richard.springer@univie.ac.at!
Reminder: Boise Extravaganza in Set Theory, June 17-19
Conference
6/13/2021
This post is an update regarding BEST, which begins next Thursday, 17 June and runs through 17 June. We are looking forward to seeing you! You can find the list of speakers and talk titles below. The latest information will always be available on the website.
BEST website: https://www.boisestate.edu/math/best/
Zoom ID 92626476913 (https://boisestate.zoom.us/j/92626476913)
Plenary speakers
David Fernández Bretón (UNAM). Hindman’s theorem as a weak version of the Axiom of Choice
Victoria Gitman (CUNY). Characterizing large cardinals via abstract logics
Jun Le Goh (Wisconsin). Inseparable pairs and recursion theory
Lynne Yengulalp (Wake Forest). Completeness, G-deltas, and games
Joseph Zielinski (North Texas). Orbit equivalence relations of some classes of non-locally compact Polish groups
Additional speakers
Filippo Calderoni (UIC). Rotation equivalence and cocycle superrigidity for compact actions
Natasha Dobrinen (Denver). Big Ramsey degrees of universal inverse limit structures
Thomas Gilton (Pittsburgh). Club stationary reflection and the special Aronszajn tree property
Osvaldo Guzmán González (UNAM). MAD families and strategically bounding forcings
Randall Holmes (Boise). An outline of a proof of the consistency of New Foundations
Martina Iannella (Udine). The complexity of convex bi-embeddability among countable linear orders
Krzysztof Kowitz (Gdańsk). Differentially compact space and Hindman space
Maxwell Levine (Freiburg). Patterns of stationary reflection
Renan Mezabarba (UFES). A characterization of productive cellularity
Aristotelis Panagiotopoulos (Münster). Dynamical obstructions to classification by (co)homology and other TSI-group invariants
Nick Ramsey (UCLA). Exact saturation in pseudo-elementary classes
Panagiotis Rouvelas (Patras). Models of predicative NF
Cory Switzer (KGRC). Tight eventually different families
Riley Thornton (UCLA). Effectivization in Borel combinatorics
Kameryn Williams (Hawaii). Coding sets into inner mantles
Jenna Zomback (UIUC). Ergodic theorems along trees
Tagged: David Fernández Bretón, Victoria Gitman, Jun Le Goh, Lynne Yengulalp, Joseph Zielinski, Filippo Calderoni, Natasha Dobrinen, Thomas Gilton, Osvaldo Guzmán González, Randall Holmes, Martina Iannella, Krzysztof Kowitz, Maxwell Levine, Renan Mezabarba, Aristotelis Panagiotopoulos, Nick Ramsey, Panagiotis Rouvelas, Cory Switzer, Riley Thornton, Kameryn Williams, Jenna Zomback
CMU logic events during coming week
Carnegie Mellon Logic Seminar
6/13/2021 11:28:38
TUESDAY, June 15, 2021
Mathematical logic seminar: 3:30 P.M., Online, James Cummings, Carnegie Mellon University
Join Zoom Meeting:
https://cmu.zoom.us/j/621951121 [
cmu.zoom.us]
Meeting ID: 621 951 121
TITLE: Homological algebra for logicians
ABSTRACT: This is part 3 of a short series of talks aimed at giving some background for Nathaniel Bannister's forthcoming seminars. Nathaniel's talks will describe his work with Bergfalk and Moore on the additivity of strong homology.
I will give a rapid overview of some necessary background in homological algebra (eg abelian categories, chain complexes, derived functors). I will assume very little background, just familiarity with basic notions in category theory (category, functor, natural transformation) and algebra (the definition of an R-module).
TUESDAY, June 15, 2021
Set Theory Reading Group: 4:30 P.M., Online, James Cummings, Carnegie Mellon University
Join Zoom Meeting:
https://cmu.zoom.us/j/621951121 [
cmu.zoom.us]
Meeting ID: 621 951 121
TITLE: Homological algebra for logicians
ABSTRACT: This is part 4 of a short series of talks aimed at giving some background for Nathaniel Bannister's forthcoming seminars. Nathaniel's talks will describe his work with Bergfalk and Moore on the additivity of strong homology.
I will give a rapid overview of some necessary background in homological algebra (eg abelian categories, chain complexes, derived functors). I will assume very little background, just familiarity with basic notions in category theory (category, functor, natural transformation) and algebra (the definition of an R-module).
THURSDAY, June 17, 2021
Ph.D. Thesis Defense: 12:00 P.M., Online, Marcos Mazari-Armida
Zoom:
https://cmu.zoom.us/j/96301869290?pwd=Qk1zS0h6ZThmUnRpbmNLNkVJSjkrQT09TITLE OF DISSERTATION: Remarks on classification theory for abstract elementary classes with applications to abelian group theory and ring theory
EXAMINERS:
Prof. Rami Grossberg (Committee Chair)
Prof. Jeremy Avigad
Prof. John Baldwin, UIC
Prof. Will Boney, Texas State
Prof. James Cummings
Barcelona Set theory Seminar
Barcelona Logic Seminar
6/6/2021 16:20:00
Dear All,
Please find attached the announcement of the next session of the Barcelona Set Theory Seminar. Feel free to distribute it.
SPEAKER: Raffaella Cutolo (Università degli Studi di Napoli Federico II)
TITLE: N-Berkeley cardinals and the two futures of set theory
DATE: 9 June 2021
TIME: 16:00 (CEST)
PLACE: The Seminar will take place online at the following address:
Best regards,
Joan
P.S.: If you do not wish to receive any more announcements, please send an email to
bagaria@ub.edu with the text “Unsubscribe”.
Joan Bagaria
ICREA Research Professor
Universitat de Barcelona
Departament de Matemàtiques i Informàtica
Gran Via de les Corts Catalanes 585
08007 Barcelona
Catalonia
Phone: +34 93 402 1609
Talk tomorrow by Piotr Szewczak (1:30 pm Toronto time)
Toronto Set Theory Seminar
6/3/2021 8:00:00
Hello everyone,
Please use the following link and, only in case that it appears, fill the form (every week) to enter the meeting. This form helps the Field Institute to know statistical data about attendance.
Here the speaker information:
Speaker: Piotr Szewczak
Date and Time: Friday, June 4th, 2021 - 1:30pm to 3:00pm
Title: Abstract colorings, games and ultrafilters
Abstract:
During the talk we consider various kinds of Ramsey-type theorems.
Bergelson and Hindman investigated finite colorings of the complete graph [N]^2 with vertices in natural numbers, involving an algebraic structure of N. It follows from their result that for each finite coloring of [N]^2, there are finite pairwise disjoint sets F1, F2, … such that each set Fn contains an arithmetic progression of length n and all edges between vertices from different sets Fn have the same color. Colorings of graphs appear also in the context of combinatorial covering properties. Scheepers proved that a set of reals X is Menger if and only if for every finite coloring of the complete graph whose vertices are open sets in X and an open omega-cover U of X (i.e., every finite subset of X is contained in a proper subset of X from the cover), there are finite pairwise disjoint subfamilies F1, F2, … of U such that the union of these families is point-infinite cover of X and all edges between vertices from different sets Fn have the same color.
The aim of the talk is to present a theorem that captures many results in a similar spirit (including mentioned above). To this end we use topological games and some special ultrafilters in the Stone—Cech compactification of semigroups. The research was motivated by the recent result of Tsaban, who extended the celebrated Hindman Finite Sum Theorem (and its high-dimensional version due to Milliken and Taylor) to covers of Menger spaces.
Talk this Friday June 4th by Piotr Szewczak (1:30 pm Toronto time)
Toronto Set Theory Seminar
6/2/2021 1:30:27
Hello everyone,
Please use the following link and, only in case that it appears, fill the form (every week) to enter the meeting. This form helps the Field Institute to know statistical data about attendance.
Here the speaker information:
Date and Time: Friday, June 4th, 2021 - 1:30pm to 3:00pm
Title: Abstract colorings, games and ultrafilters
Abstract:
During the talk we consider various kinds of Ramsey-type theorems.
Bergelson and Hindman investigated finite colorings of the complete graph [N]^2 with vertices in natural numbers, involving an algebraic structure of N. It follows from their result that for each finite coloring of [N]^2, there are finite pairwise disjoint sets F1, F2, … such that each set Fn contains an arithmetic progression of length n and all edges between vertices from different sets Fn have the same color. Colorings of graphs appear also in the context of combinatorial covering properties. Scheepers proved that a set of reals X is Menger if and only if for every finite coloring of the complete graph whose vertices are open sets in X and an open omega-cover U of X (i.e., every finite subset of X is contained in a proper subset of X from the cover), there are finite pairwise disjoint subfamilies F1, F2, … of U such that the union of these families is point-infinite cover of X and all edges between vertices from different sets Fn have the same color.
The aim of the talk is to present a theorem that captures many results in a similar spirit (including mentioned above). To this end we use topological games and some special ultrafilters in the Stone—Cech compactification of semigroups. The research was motivated by the recent result of Tsaban, who extended the celebrated Hindman Finite Sum Theorem (and its high-dimensional version due to Milliken and Taylor) to covers of Menger spaces.
Barcelona Set theory Seminar
Barcelona Logic Seminar
5/30/2021 16:07:14
Dear All,
Please find attached the announcement of the next session of the Barcelona Set Theory Seminar. Feel free to distribute it.
SPEAKER: Michał Tomasz Godziszewski (University of Warsaw)
TITLE: The Multiverse, Recursive Saturation and Well-Foundedness Mirage
DATE: 2 June 2021
TIME: 16:00 (CEST)
PLACE: The Seminar will take place online at the following address:
Best regards,
Joan
P.S.: If you do not wish to receive any more announcements, please send an email to
bagaria@ub.edu with the text “Unsubscribe”.
Joan Bagaria
ICREA Research Professor
Universitat de Barcelona
Departament de Matemàtiques i Informàtica
Gran Via de les Corts Catalanes 585
08007 Barcelona
Catalonia
Phone: +34 93 402 1609
Two events on June 8
Carnegie Mellon Logic Seminar
5/30/2021 12:38:14
TUESDAY, June 8, 2021
Mathematical logic seminar: 3:30 P.M., Online, James Cummings, Carnegie
Mellon University
Join Zoom Meeting: https://cmu.zoom.us/j/621951121 [cmu.zoom.us]
Meeting ID: 621 951 121
TITLE: Title: Homological algebra for logicians
ABSTRACT: This is part 1 of a short series of talks aimed at giving some
background for Nathaniel Bannister's forthcoming seminars. Nathaniel's
talks will describe his work with Bergfalk and Moore on the additivity of
strong homology.
I will give a rapid overview of some necessary background in homological
algebra (eg abelian categories, chain complexes, derived functors). I will
assume very little background, just familiarity with basic notions in
category theory (category, functor, natural transformation) and algebra
(the definition of an R-module)
TUESDAY, June 8, 2021
Set Theory Reading Group: 4:30 P.M., Online, James Cummings, Carnegie
Mellon University
Join Zoom Meeting: https://cmu.zoom.us/j/621951121 [cmu.zoom.us]
Meeting ID: 621 951 121
TITLE: Title: Homological algebra for logicians
ABSTRACT: This is part 2 of a short series of talks aimed at giving some
background for Nathaniel Bannister's forthcoming seminars. Nathaniel's
talks will describe his work with Bergfalk and Moore on the additivity of
strong homology.
I will give a rapid overview of some necessary background in homological
algebra (eg abelian categories, chain complexes, derived functors). I will
assume very little background, just familiarity with basic notions in
category theory (category, functor, natural transformation) and algebra
(the definition of an R-module)
Talk Tomorrow by Boban Velickovic at 1 30 (Toronto time)
Toronto Set Theory Seminar
5/27/2021 13:00:00
Hello everyone,
Please
use the following link and, only in case that it appears, fill the form (every week) to enter the
meeting. This form helps the Field Institute to know statistical data
about attendance.
Here the speaker information:
Speaker: Boban Velickovic
Date and Time: Friday, May 28th, 2021 - 1:30pm to 3:00pm
Title:
Non vanishing higher derived limits
Abstract:
In the study of strong homology Mardesic and Prasolov isolated a
certain inverse system of abelian groups A indexed by functions from
\omega to \omega.
They showed that if strong homology is
additive on a class of spaces containing closed subsets of Euclidean
spaces then the higher derived limits lim^n A must vanish for n >0.
They
also proved that under the Continuum Hypothesis lim^1 A does not
vanish. On the other hand Down, Simon and Vaughan showed that under PFA
lim^1 A=0
The question whether lim^n A vanishes higher n has
attracted considerable attention recently. First, Bergfalk shows that
it was consistent lim^2 A does not vanish.
Later Bergfalk and
Lambie-Hanson showed that, assuming modest large cardinal axioms, lim^n
A vanishes for all n. The large cardinal assumption was later removed
by Bergfalk, Hrusak and Lambie-Hanson. We complete the picture by
showing that, for any n>0, it is relatively consistent with ZFC that
lim^n A is non zero.
This is joint work with Alessandro Vignati.
Iván Ongay Valverde (he/his)
(KGRC) research seminar talk on Thursday, May 27
Kurt Godel Research Center
5/25/2021 10:44:13
Research seminar
Kurt Gödel Research Center
Thursday, May 27
"Independent families and singular cardinals"
Diana Carolina Montoya (KGRC)
In this talk, we will discuss the concept of independent families for
uncountable cardinals. First, we will mention a summary of results
regarding the existence of such families in the case of an uncountable
regular cardinal. In the second part, we focus on the singular case and
present two results of ours.
This is joint work with Omer Ben-Neria.
Time and Place
Talk at 3:00pm via Zoom: This talk will be given via Zoom. If you have not
received the meeting link by the day before the talk, please contact
richard.springer@univie.ac.at!
Please note: There will be no talk in the research seminar next Thursday,
June 3 (Corpus Christi).
An interesting series of talks for grad students
Toronto Set Theory Seminar
5/25/2021 9:00:00
Hello everyone,
Vera
Fischer is organizing a series of short talks intended for graduate students.
The
idea of the talks is one short talk once a week, with the idea to
introduce
some areas of set theory to the students.
Interested
students should just send Vera a short email and she will add
them
to the list of participants. vera.fischer@univie.ac.at
The time is not optimal for people in the american continent time zones
(it
is 9:30am CET, Fridays, May 28-June 18), but she will record the
talks
for those who want to hear them at a later point. Here isthe
program until the end of the semester.
https://sites.google.com/view/short-talks-logic-uni-wien/home
Iván Ongay Valverde (he/his)
Talk Friday May 27th (this friday) by Boban Velickovic at 1 30 (Toronto time)
Toronto Set Theory Seminar
5/24/2021 15:47:43
Hello everyone,
Please
use the following link and, only in case that it appears, fill the form (every week) to enter the
meeting. This form helps the Field Institute to know statistical data
about attendance.
Here the speaker information:
Speaker: Boban Velickovic
Date and Time: Friday, May 28th, 2021 - 1:30pm to 3:00pm
Title:
Non vanishing higher derived limits
Abstract:
In the study of strong homology Mardesic and Prasolov isolated a
certain inverse system of abelian groups A indexed by functions from
\omega to \omega.
They showed that if strong homology is
additive on a class of spaces containing closed subsets of Euclidean
spaces then the higher derived limits lim^n A must vanish for n >0.
They
also proved that under the Continuum Hypothesis lim^1 A does not
vanish. On the other hand Down, Simon and Vaughan showed that under PFA
lim^1 A=0
The question whether lim^n A vanishes higher n has
attracted considerable attention recently. First, Bergfalk shows that
it was consistent lim^2 A does not vanish.
Later Bergfalk and
Lambie-Hanson showed that, assuming modest large cardinal axioms, lim^n
A vanishes for all n. The large cardinal assumption was later removed
by Bergfalk, Hrusak and Lambie-Hanson. We complete the picture by
showing that, for any n>0, it is relatively consistent with ZFC that
lim^n A is non zero.
This is joint work with Alessandro Vignati.
Iván Ongay Valverde (he/his)
Barcelona Set theory Seminar
Barcelona Logic Seminar
5/23/2021 12:18:07
Dear All,
Please find attached the announcement of the next session of the Barcelona Set Theory Seminar. Feel free to distribute it.
SPEAKER: David Asperó (UEA, Norwich)
TITLE: Around (*)
DATE: 26 May 2021
TIME: 16:00 (CEST)
PLACE: The Seminar will take place online at the following address:
Best regards,
Joan
P.S.: If you do not wish to receive any more announcements, please send an email to
bagaria@ub.edu with the text “Unsubscribe”.
Joan Bagaria
ICREA Research Professor
Universitat de Barcelona
Departament de Matemàtiques i Informàtica
Gran Via de les Corts Catalanes 585
08007 Barcelona
Catalonia
Phone: +34 93 402 1609
Barcelona Set theory Seminar
Barcelona Logic Seminar
5/23/2021 12:17:10
Dear All,
Please find attached the announcement of the next session of the Barcelona Set Theory Seminar. Feel free to distribute it.
SPEAKER: David Asperó (UEA, Norwich)
TITLE: Around (*)
DATE: 26 May 2021
TIME: 16:00 (CEST)
PLACE: The Seminar will take place online at the following address:
Best regards,
Joan
P.S.: If you do not wish to receive any more announcements, please send an email to
bagaria@ub.edu with the text “Unsubscribe”.
Joan Bagaria
ICREA Research Professor
Universitat de Barcelona
Departament de Matemàtiques i Informàtica
Gran Via de les Corts Catalanes 585
08007 Barcelona
Catalonia
Phone: +34 93 402 1609
Barcelona Set theory Seminar
Barcelona Logic Seminar
5/23/2021 12:16:48
Dear All,
Please find attached the announcement of the next session of the Barcelona Set Theory Seminar. Feel free to distribute it.
SPEAKER: David Asperó (UEA, Norwich)
TITLE: Around (*)
DATE: 26 May 2021
TIME: 16:00 (CEST)
PLACE: The Seminar will take place online at the following address:
Best regards,
Joan
P.S.: If you do not wish to receive any more announcements, please send an email to
bagaria@ub.edu with the text “Unsubscribe”.
Joan Bagaria
ICREA Research Professor
Universitat de Barcelona
Departament de Matemàtiques i Informàtica
Gran Via de les Corts Catalanes 585
08007 Barcelona
Catalonia
Phone: +34 93 402 1609
(KGRC) research seminar talk on Thursday, May 20
Kurt Godel Research Center
5/17/2021 11:07:09
Research seminar
Kurt Gödel Research Center
Thursday, May 20
"Extensions of inner models of ZFC"
Lev Bukovsky
(Pavol Jozef Šafárik University in Košice, Slovakia)
I would like to present some results of members of Vopěnka's seminary in
1960's and 1970's (B. Balcar, P. Vopěnka, P. Hájek and me), which were
either not published or published in the language of semisets theory.
Consequently, those results are not commonly known.
Time and Place
Talk at 3:00pm via Zoom: This talk will be given via Zoom. If you have not
received the meeting link by the day before the talk, please contact
richard.springer@univie.ac.at!
Barcelona Set theory Seminar
Barcelona Logic Seminar
5/17/2021 3:05:04
Dear All,
Please find attached the announcement of the next session of the Barcelona Set Theory Seminar. Feel free to distribute it.
SPEAKER: Luca Incurvati (Amsterdam)
TITLE: Iteration, dependence and structuralism
DATE: 19 May 2021
TIME: 16:00 (CEST)
PLACE: The Seminar will take place online at the following address:
Best regards,
Joan
P.S.: If you do not wish to receive any more announcements, please send an email to
bagaria@ub.edu with the text “Unsubscribe”.
Joan Bagaria
ICREA Research Professor
Universitat de Barcelona
Departament de Matemàtiques i Informàtica
Gran Via de les Corts Catalanes 585
08007 Barcelona
Catalonia
Phone: +34 93 402 1609
This Week in Logic at CUNY
This Week in Logic at CUNY
5/9/2021 22:30:00
This Week in Logic at CUNY:
- - - - Monday, May 3, 2021 - - - -
Logic and Metaphysics Workshop
Date: Monday, May 3rd, 4.15-6.15 (NY time)
Graziana Ciola (Radboud Nijmegen).
Title: Marsilius of Inghen, John Buridan and the Semantics of Impossibility
Abstract: In the 14th-century, imaginable yet in some sense impossible non-entities start playing a crucial role in logic, natural philosophy and metaphysics. Throughout the later middle ages and well into early modernity, Marsilius of Inghen’s name comes to be unavoidably associated with the semantics of imaginable impossibilities in most logical and metaphysical discussions. In this paper I analyse Marsilius of Inghen’s semantic treatment of impossible referents, through a comparison with John Buridan’s. While in many ways Marsilius is profoundly influenced by Buridan’s philosophy, his semantic analysis of impossibilia is radically different from Buridan’s. Overall, Buridan tends to analyse away impossible referents in terms of complex concepts by combining possible simple individual parts. Marsilius, on the one hand, treats impossibilia as imaginable referents that are properly unitary; on the other hand, he extends the scope of his modal semantics beyond the inclusion of merely relative impossibilities, allowing for a full semantic treatment of absolute impossibilities as well. Here, I will explore the extent of these differences between Buridan’s and Marsilius of Inghen’s semantics, their presuppositions, and their respective conceptual impact on early modern philosophy of logic and mathematics.
- - - - Tuesday, May 4, 2021 - - - -
- - - - Wednesday, May 5, 2021 - - - -
- - - - Thursday, May 6, 2021 - - - -
Philog Seminar
CUNY Graduate Center
Thursday May 6, 2021, 6:30 PM
Ada Coronado
Nietzsche on, Logic, Philosophy, and Moral Values
Introduction: Studies in logic rarely ever mention Fredrich Nietzsche. There is very little literature on Nietzsche’s critique of classical logic and there is no indication that he followed the developments that were occurring in the field in the 19th century by contemporaneous thinkers such as George Boole, Frege, or Augustus De Morgan. Yet, logic is central to Nietzsche’s seminal work Beyond Good and Evil: Prelude to a Philosophy of the Future, henceforth referred to as BGE. Believing that classical logic falsely reinforces the religious promise of absolutism and certainty, Nietzsche rejects the possibility of a priori truths qua truth, but embraces logic to the extent that he considers it the vehicle that systematically discharges a philosopher’s energy and morality onto the world.
In this talk I consider Nietzsche’s critique of moral values as they relate to his rejection of both a priori truths and the semantic principle of bivalence, or what he calls the “faith of opposite values”. I argue that Nietzsche’s approach to philosophy, logic, and moral values heralds the future philosophical significance of multivalent systems and paraconsistent logic.
A Zoom link will be posted on
https://philog.arthurpaulpedersen.org/- - - - Friday, May 7, 2021 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, May 7, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. Benjamin Goodman, CUNY
Woodin's Extender Algebra
This oral exam talk will present a proof of Woodin's result that every real number is generic over some iterated ultrapower of any model with a Woodin cardinal. No fine structure theory will be used, and there will be a brief introduction to iteration trees.
Next Week in Logic at CUNY:
- - - - Monday, May 10, 2021 - - - -
Logic and Metaphysics Workshop
Date: Monday, May 10th, 4.15-6.15 (NY time)
Filippo Casati (Lehigh)
Title: Heidegger on the Limits and Possibilities of Human Thinking
Abstract: In my talk, I will address what Heidegger calls ‘the basic problem’ of his philosophy, that is, the alleged incompatibility between the notion of Being, our thinking, and logic. First of all, I will discuss some of the ways in which Heideggerians have dealt with this incompatibility by distinguishing what I call the irrationalist and rationalist interpretation. Secondly, I will argue that these two interpretations face both exegetical and philosophical problems. To conclude, I will defend an alternative way to address the incompatibility between the notion of Being, our thinking, and logic. I will argue that, in some of his late works, Heidegger seems to suggest that the real problem lies in the philosophical illusion that we can actually assess the limits of our thinking and, therewith, our logic. Heidegger’s philosophy, I deem, wants to free us from such a philosophical illusion by delivering an experience which reminds us that our thinking is something we can never ‘look at from above’ in order to either grasp its limits or realize that it has no limits whatsoever.
- - - - Tuesday, May 11, 2021 - - - -
- - - - Wednesday, May 12, 2021 - - - -
- - - - Thursday, May 13, 2021 - - - -
Philog Seminar
CUNY Graduate Center
Thursday May 13, 2021, 6:30 PM
Eric Pacuit, University of Maryland
Epistemic Networks for Imprecise Agents
Abstract: What is the best form for social influence to take? Are all policies which aim to increase the amount of interaction over a particular issue likely to be successful in their aims? In this talk, I will survey some models that have been proposed by economists and social epistemologists to address these questions. These models typically assume that the agents have precise beliefs about the proposition that they are trying to learn. However, in many learning situations, at least some of the agents may have imprecise beliefs about the proposition that they are trying to learn. The second part of the talk will report on some work in progress with Paul Pedersen about how best to design communication networks when some agents have imprecise beliefs.
Eric Pacuit is an associate professor in the Department of Philosophy at the University of Maryland. Prior to coming to Maryland, Eric did his graduate work at the City University of New York Graduate Center, and was a postdoctoral researcher at the Institute for Logic, Language and Computation at the University of Amsterdam and in the Departments of Philosophy and Computer Science at Stanford University. Eric’s primary research interests are in logic (especially modal logic), game theory, social choice theory, and formal and social epistemology. His research has been funded by the Natural Science Foundation and a Vidi grant from the Dutch science foundation (NWO).
- - - - Friday, May 14, 2021 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, May 14, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. Corey Switzer, University of Vienna
Tight Maximal Eventually Different Families
Maximal almost disjoint (MAD) families and their relatives have been an important area of combinatorial and descriptive set theory since at least the 60s. In this talk I will discuss some relatives of MAD families, focussing on eventually different families of functions f:ω→ωf:ω→ω and eventually different sets of permutations p∈S(ω)p∈S(ω). In the context of MAD families it has been fruitful to consider various strengthenings of the maximality condition to obtain several flavors of 'strongly' MAD families. One such strengthening that has proved useful in recent literature is that of tightness. Tight MAD families are Cohen indestructible and come with a properness preservation theorem making them nice to work with in iterated forcing contexts.
I will introduce a version of tightness for maximal eventually different families of functions f:ω→ωf:ω→ω and maximal eventually different families of permutations p∈S(ω)p∈S(ω) respectively. These tight eventually different families share a lot of the nice, forcing theoretic properties of tight MAD families. Using them, I will construct explicit witnesses to ae=ap=ℵ1ae=ap=ℵ1 in many known models of set theory where this equality was either not known or only known by less constructive means. Working over LL we can moreover have the witnesses be Π11Π11 which is optimal for objects of size ℵ1ℵ1 in models where CHCH fails. These results simultaneously strengthen several known results on the existence of definable maximal sets of reals which are indestructible for various definable forcing notions. This is joint work with Vera Fischer.
Next Week in Logic at CUNY:
- - - - Monday, May 17, 2021 - - - -
- - - - Tuesday, May 18, 2021 - - - -
- - - - Wednesday, May 19, 2021 - - - -
- - - - Thursday, May 20, 2021 - - - -
- - - - Friday, May 21, 2021 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, May 21, 1pm
The seminar will take place virtually at 1pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. Omer Ben-Neria, Hebrew University
TBA
- - - - Other Logic News - - - -
- - - - Web Site - - - -"Find us on the web at: nylogic.github.io(site designed, built & maintained by Victoria Gitman)"-------- ADMINISTRIVIA --------To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.
Barcelona Set theory Seminar
Barcelona Logic Seminar
5/9/2021 15:30:28
Dear All,
Please find attached the announcement of the next session of the Barcelona Set Theory Seminar. Feel free to distribute it.
SPEAKER: Sakaé Fuchino (Kobe)
TITLE: Generically supercompact cardinals as reflection principles
DATE: 12 April 2021
TIME: 16:00 (CEST)
PLACE: The Seminar will take place online at the following address:
Best regards,
Joan
P.S.: If you do not wish to receive any more announcements, please send an email to
bagaria@ub.edu with the text “Unsubscribe”.
Joan Bagaria
ICREA Research Professor
Universitat de Barcelona
Departament de Matemàtiques i Informàtica
Gran Via de les Corts Catalanes 585
08007 Barcelona
Catalonia
Phone: +34 93 402 1609
All links to today talk work (preferably, use the one to fill the form)
Toronto Set Theory Seminar
5/7/2021 13:02:19
Hello everyone,
Our webmaster is a magician, so any of the links I have sent will lead to the seminar talk.
Nevertheless, since the fields institute like to have general data about who attends, the following link will be the one that will lead you to the registration form and then to the talk. This is the best one to use (that, curiously, is the same as in the very first email):
That is the link that you can also find in the webpage. Thanks to Miles for his quick and awesome help.
Best
Iván Ongay Valverde (he/his)
Today (Friday, 7th) talk by Itsvan Juhasz
Toronto Set Theory Seminar
5/7/2021 8:00:00
Hello everyone,
Please
use the following link and, only in case that it appears, fill the form (every week) to enter the
meeting. This form helps the Field Institute to know statistical data
about attendance. This is the correct link.
Here the speaker information:
Date and Time: Friday, May 7th, 2021 - 1:30pm to 3:00pm
Title: Anti-Urysohn spaces
Iván Ongay Valverde (he/his)
Talk Tomorrow by Itsvan Juhasz at 1 30 pm (Toronto time)
Toronto Set Theory Seminar
5/7/2021 0:29:09
I owe an apology to everyone. Our recurring meeting ended without me noticing, for this session we will use the following link. Most likely the registration form will not appear.
I'll talk with the webmaster to fix all the issues.
Fields Seminars 1 is inviting you to a scheduled Zoom meeting.
Topic: Set Theory Seminar
Time: 1:30-3:00 pm Friday May 7th
Join Zoom Meeting
https://zoom.us/j/97109130026?pwd=a2VMVUJBMmZweXU4a0ZnaE02NmJvZz09Meeting ID: 971 0913 0026
Passcode: 729463
One tap mobile
+17789072071,,97109130026# Canada
+14388097799,,97109130026# Canada
Dial by your location
+1 778 907 2071 Canada
+1 438 809 7799 Canada
+1 587 328 1099 Canada
+1 647 374 4685 Canada
+1 647 558 0588 Canada
Meeting ID: 971 0913 0026
Find your local number:
https://zoom.us/u/abXb8IbMLtIván Ongay Valverde (he/his)
Hello everyone,
Please
use the following link and fill the form (every week) to enter the
meeting. This form helps the Field Institute to know statistical data
about attendance.
Here the speaker information:
Date and Time: Friday, May 7th, 2021 - 1:30pm to 3:00pm
Title: Anti-Urysohn spaces
Iván Ongay Valverde (he/his)
Talk Tomorrow by Itsvan Juhasz at 1 30 pm (Toronto time)
Toronto Set Theory Seminar
5/6/2021 20:00:02
Hello everyone,
Please
use the following link and fill the form (every week) to enter the
meeting. This form helps the Field Institute to know statistical data
about attendance.
Here the speaker information:
Date and Time: Friday, May 7th, 2021 - 1:30pm to 3:00pm
Title: Anti-Urysohn spaces
Iván Ongay Valverde (he/his)
This Week in Logic at CUNY
This Week in Logic at CUNY
5/3/2021 11:41:52
This Week in Logic at CUNY:
- - - - Monday, May 3, 2021 - - - -
Logic and Metaphysics Workshop
Date: Monday, May 3rd, 4.15-6.15 (NY time)
Graziana Ciola (Radboud Nijmegen).
Title: Marsilius of Inghen, John Buridan and the Semantics of Impossibility
Abstract: In the 14th-century, imaginable yet in some sense impossible non-entities start playing a crucial role in logic, natural philosophy and metaphysics. Throughout the later middle ages and well into early modernity, Marsilius of Inghen’s name comes to be unavoidably associated with the semantics of imaginable impossibilities in most logical and metaphysical discussions. In this paper I analyse Marsilius of Inghen’s semantic treatment of impossible referents, through a comparison with John Buridan’s. While in many ways Marsilius is profoundly influenced by Buridan’s philosophy, his semantic analysis of impossibilia is radically different from Buridan’s. Overall, Buridan tends to analyse away impossible referents in terms of complex concepts by combining possible simple individual parts. Marsilius, on the one hand, treats impossibilia as imaginable referents that are properly unitary; on the other hand, he extends the scope of his modal semantics beyond the inclusion of merely relative impossibilities, allowing for a full semantic treatment of absolute impossibilities as well. Here, I will explore the extent of these differences between Buridan’s and Marsilius of Inghen’s semantics, their presuppositions, and their respective conceptual impact on early modern philosophy of logic and mathematics.
- - - - Tuesday, May 4, 2021 - - - -
- - - - Wednesday, May 5, 2021 - - - -
- - - - Thursday, May 6, 2021 - - - -
Philog Seminar
CUNY Graduate Center
Thursday May 6, 2021, 6:30 PM
Ada Coronado
Nietzsche on, Logic, Philosophy, and Moral Values
Introduction: Studies in logic rarely ever mention Fredrich Nietzsche. There is very little literature on Nietzsche’s critique of classical logic and there is no indication that he followed the developments that were occurring in the field in the 19th century by contemporaneous thinkers such as George Boole, Frege, or Augustus De Morgan. Yet, logic is central to Nietzsche’s seminal work Beyond Good and Evil: Prelude to a Philosophy of the Future, henceforth referred to as BGE. Believing that classical logic falsely reinforces the religious promise of absolutism and certainty, Nietzsche rejects the possibility of a priori truths qua truth, but embraces logic to the extent that he considers it the vehicle that systematically discharges a philosopher’s energy and morality onto the world.
In this talk I consider Nietzsche’s critique of moral values as they relate to his rejection of both a priori truths and the semantic principle of bivalence, or what he calls the “faith of opposite values”. I argue that Nietzsche’s approach to philosophy, logic, and moral values heralds the future philosophical significance of multivalent systems and paraconsistent logic.
A Zoom link will be posted on
https://philog.arthurpaulpedersen.org/- - - - Friday, May 7, 2021 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, May 7, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. Benjamin Goodman, CUNY
Woodin's Extender Algebra
This oral exam talk will present a proof of Woodin's result that every real number is generic over some iterated ultrapower of any model with a Woodin cardinal. No fine structure theory will be used, and there will be a brief introduction to iteration trees.
Next Week in Logic at CUNY:
- - - - Monday, May 10, 2021 - - - -
Logic and Metaphysics Workshop
Date: Monday, May 10th, 4.15-6.15 (NY time)
Filippo Casati (Lehigh)
Title: Heidegger on the Limits and Possibilities of Human Thinking
Abstract: In my talk, I will address what Heidegger calls ‘the basic problem’ of his philosophy, that is, the alleged incompatibility between the notion of Being, our thinking, and logic. First of all, I will discuss some of the ways in which Heideggerians have dealt with this incompatibility by distinguishing what I call the irrationalist and rationalist interpretation. Secondly, I will argue that these two interpretations face both exegetical and philosophical problems. To conclude, I will defend an alternative way to address the incompatibility between the notion of Being, our thinking, and logic. I will argue that, in some of his late works, Heidegger seems to suggest that the real problem lies in the philosophical illusion that we can actually assess the limits of our thinking and, therewith, our logic. Heidegger’s philosophy, I deem, wants to free us from such a philosophical illusion by delivering an experience which reminds us that our thinking is something we can never ‘look at from above’ in order to either grasp its limits or realize that it has no limits whatsoever.
- - - - Tuesday, May 11, 2021 - - - -
- - - - Wednesday, May 12, 2021 - - - -
- - - - Thursday, May 13, 2021 - - - -
- - - - Friday, May 14, 2021 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, May 14, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. Corey Switzer, University of Vienna
- - - - Other Logic News - - - -
- - - - Web Site - - - -"Find us on the web at: nylogic.github.io(site designed, built & maintained by Victoria Gitman)"-------- ADMINISTRIVIA --------To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.
(KGRC) research seminar talk on Thursday, May 6
Kurt Godel Research Center
5/3/2021 10:29:04
Research seminar
Kurt Gödel Research Center
Thursday, May 6
"Absolute model companionship, the continuum problem, and forcibility"
Matteo Viale
(Università degli Studi di Torino, Italy)
Absolute model companionship (AMC) is a strengthening of model
companionship defined as follows: For a theory $T$,
$T_{\exists\vee\forall}$ denotes the logical consequences of $T$ which are
boolean combinations of universal sentences. $T^*$ is the AMC of $T$ if it
is model complete and $T_{\exists\vee\forall}=T^*_{\exists\vee\forall}$.
The theory $\mathsf{ACF}$ of algebraically closed field is the model
companion of the theory $\mathsf{Fields}$ of fields but not its AMC as
$\exists x(x^2+1=0)\in
\mathsf{ACF}_{\exists\vee\forall}\steaminess\mathsf{Fields}_{\exists\vee\forall}$.
Any model complete theory $T$ is the AMC of $T_{\exists\vee\forall}$.
We use AMC to study the continuum problem and to gauge the expressive
power of forcing. We show that (a definable version of)
$2^{\aleph_0}=\aleph_2$ is the unique solution to the continuum problem
which can be in the AMC of a \emph{partial Morleyization} of the
$\in$-theory $\ZFC$ enriched with large cardinal axioms. We also show that
(assuming large cardinals) forcibility overlaps with the apparently
stronger notion of consistency for any mathematical problem $\psi$
expressible as a $\Pi_2$-sentence of a (very large fragment of) third
order arithmetic ($\CH$, the Suslin hypothesis, the Whitehead conjecture
for free groups, are a small sample of such problems $\psi$).
Partial Morleyizations can be described as follows: let $F_{\tau}$ be the
set of first order $\tau$-formulae; for $A\subseteq F_\tau$, $\tau_A$ is
the expansion of $\tau$ adding atomic relation symbols $R_\phi$ for all
formulae $\phi$ in $A$ and $T_{\tau,A}$ is the $\tau_A$-theory asserting
that each $\tau$-formula $\phi(\vec{x})\in A$ is logically equivalent to
the corresponding atomic formula $R_\phi(\vec{x})$. For a $\tau$-theory
$T$, $T+T_{\tau,A}$ is the \emph{partial Morleyization} of $T$ induced by
$A\subseteq F_\tau$.
Time and Place
Talk at 3:00pm via Zoom: This talk will be given via Zoom. If you have not
received the meeting link by the day before the talk, please contact
richard.springer@univie.ac.at!
(KGRC) research seminar talk on Thursday, April 29
Kurt Godel Research Center
4/26/2021 11:59:30
Research seminar
Kurt Gödel Research Center
Thursday, April 29
"Fullness and mixing property for boolean valued models"
Moreno Pierobon
(Università di Pisa, Italy)
Besides being one of the classical approaches to forcing, boolean valued models
provide a flexible tool to produce a variety of structures.
In this talk, we will investigate in details the fullness property and the
mixing property for boolean valued models. The former is necessary to control
the semantics when quotienting a boolean valued model by an ultrafilter. The
latter implies the former and it is easier to check.
We will show that not every model is full, and the mixing property in not
equivalent to fullness. Moreover, we will improve the classical Łoś Theorem for
boolean valued models.
In the end, we will give a simple characterization of the mixing property using
étalé spaces. This last result is an easy corollary of a more general study we
made on the categorical equivalence between boolean valued models and
presheaves.
This is a joint work with Matteo Viale.
Time and Place
Talk at 3:00pm via Zoom: This talk will be given via Zoom. If you have not
received the meeting link by the day before the talk, please contact
richard.springer@univie.ac.at!
This Week in Logic at CUNY
This Week in Logic at CUNY
4/25/2021 21:48:27
This Week in Logic at CUNY:
- - - - Monday, Apr 26, 2021 - - - -
Logic and Metaphysics Workshop
Date: Monday, April 26th, 4.15-6.15 (NY time)
Rohan French (UC Davis).
Title: Non-Classical Metatheory
Abstract: A common line of thinking has it that proponents of non-classical logics who claim that their preferred logic L gives the correct account of validity, while at the same time giving proofs of theorems about L using classical logic, are in some sense being insincere in their claim that L is the correct logic. This line of thought quite naturally motivates a correctness requirement on a non-classical logic L: that it be able to provide internally acceptable proofs of its main metatheorems. Of central importance amongst such metatheorems will typically be soundness and completeness results, such results being apt to play important roles in arguments showing that a given logic gives the correct account of validity. On the face of it this sounds like a reasonable requirement, but determining its precise content requires us to settle two important conceptual questions: what counts as a completeness proof for a logic, and what does it mean for a result to be internally acceptable? To get clearer on this issue we will look at three different results which have some claim to being internally acceptable soundness and completeness proofs, focusing for ease of comparison on the case of intuitionistic propositional logic, examining the extent to which they can be said to provide internally acceptable soundness and completeness results.
- - - - Tuesday, Apr 27, 2021 - - - -
Models of Peano Arithmetic (MOPA)
Tuesday, April 20, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. Dave Marker, University of Illinois at Chicago
Real closures of ω1ω1-like models of PA
D'Aquino, Knight and Starchenko showed the real closure of a model of Peano Arithmetic is recursively saturated. Thus any two countable models of PA with the same standard system have isomorphic real closures. Charlie Steinhorn, Jim Schmerl and I showed that even for ω1ω1-like model of PA the situation is very different. We construct 2ℵ12ℵ1 recursively saturated elementarily equivalent ω1ω1-like models of PA with the same standard system and non-isomorphic real closures.
- - - - Wednesday, Apr 28, 2021 - - - -
- - - - Thursday, Apr 29, 2021 - - - -
- - - - Friday, Apr 30, 2021 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, Apr 30, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. Elliot Glazer, Harvard University
Paradoxes of perfectly small sets
We define a set of real numbers to be perfectly small if it has perfectly many disjoint translates. Such sets have a strong intuitive claim to being probabilistically negligible, yet no non-trivial measure assigns them all a value of 0. We will prove from a moderate amount of choice that any total extension of Lebesgue measure concentrates on a perfectly small set, suggesting that for any such measure, translation-invariance fails 'as badly as possible.' From the ideas of this proof, we will also derive analogues of well-known paradoxes of randomness, specifically Freiling's symmetry paradox and the infinite prisoner hat puzzle, in terms of perfectly small sets. Finally, we discuss how these results constrain what a paradox-free set theory can look like and some related open questions.
Next Week in Logic at CUNY:
- - - - Monday, May 3, 2021 - - - -
Logic and Metaphysics Workshop
Date: Monday, May 3rd, 4.15-6.15 (NY time)
Graziana Ciola (Radboud Nijmegen).
Title: Marsilius of Inghen, John Buridan and the Semantics of Impossibility
Abstract: In the 14th-century, imaginable yet in some sense impossible non-entities start playing a crucial role in logic, natural philosophy and metaphysics. Throughout the later middle ages and well into early modernity, Marsilius of Inghen’s name comes to be unavoidably associated with the semantics of imaginable impossibilities in most logical and metaphysical discussions. In this paper I analyse Marsilius of Inghen’s semantic treatment of impossible referents, through a comparison with John Buridan’s. While in many ways Marsilius is profoundly influenced by Buridan’s philosophy, his semantic analysis of impossibilia is radically different from Buridan’s. Overall, Buridan tends to analyse away impossible referents in terms of complex concepts by combining possible simple individual parts. Marsilius, on the one hand, treats impossibilia as imaginable referents that are properly unitary; on the other hand, he extends the scope of his modal semantics beyond the inclusion of merely relative impossibilities, allowing for a full semantic treatment of absolute impossibilities as well. Here, I will explore the extent of these differences between Buridan’s and Marsilius of Inghen’s semantics, their presuppositions, and their respective conceptual impact on early modern philosophy of logic and mathematics.
- - - - Tuesday, May 4, 2021 - - - -
- - - - Wednesday, May 5, 2021 - - - -
- - - - Thursday, May 6, 2021 - - - -
- - - - Friday, May 7, 2021 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, May 7, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. Benjamin Goodman, CUNY
- - - - Other Logic News - - - -
- - - - Web Site - - - -"Find us on the web at: nylogic.github.io(site designed, built & maintained by Victoria Gitman)"-------- ADMINISTRIVIA --------To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.
Barcelona Set theory Seminar
Barcelona Logic Seminar
4/25/2021 13:34:25
Dear All,
Please find attached the announcement of the next session of the Barcelona Set Theory Seminar. Feel free to distribute it.
SPEAKER: Yair Hayut (Hebrew University, Jerusalem)
TITLE: omega-strongly measurable cardinals
DATE: 28 April 2021
TIME: 16:00 (CEST)
PLACE: The Seminar will take place online at the following address:
Best regards,
Joan
P.S.: If you do not wish to receive any more announcements, please send an email to
bagaria@ub.edu with the text “Unsubscribe”.
Joan Bagaria
ICREA Research Professor
Universitat de Barcelona
Departament de Matemàtiques i Informàtica
Gran Via de les Corts Catalanes 585
08007 Barcelona
Catalonia
Phone: +34 93 402 1609
Two CMU events on Tuesday, April 27
Carnegie Mellon Logic Seminar
4/20/2021 23:19:21
TUESDAY, April 27, 2021
Mathematical logic seminar: 3:30 P.M., Online, Omer Ben-Neria, The Hebrew
University of Jerusalem
Join Zoom Meeting: https://cmu.zoom.us/j/621951121 [cmu.zoom.us]
Meeting ID: 621 951 121
TITLE: Tree-like scales and free subsets of set theoretic algebras, part 1
ABSTRACT: In his PhD thesis, Luis Pereira isolated and developed several
principles of singular cardinals that emerge from Shelah's PCF theory;
principles which involve properties of scales, such as the inexistence of
continuous Tree Like scales, and properties of internally approachable
structures such as the Approachable Free Subset Property. In the first
talk, I will discuss these principles and their relations, and present new
results from a joint work with Dominik Adolf concerning their consistency
and consistency strength. The second talk will focus on the extender-based
Prikry forcing and its connection with these principles.
TUESDAY, April 27, 2021
Set Theory Reading Group: 4:30 P.M., Online, Omer Ben-Neria, The Hebrew
University of Jerusalem
Join Zoom Meeting: https://cmu.zoom.us/j/621951121 [cmu.zoom.us]
Meeting ID: 621 951 121
TITLE: Tree-like scales and free subsets of set theoretic algebras, part 2
ABSTRACT: In his PhD thesis, Luis Pereira isolated and developed several
principles of singular cardinals that emerge from Shelah's PCF theory;
principles which involve properties of scales, such as the inexistence of
continuous Tree Like scales, and properties of internally approachable
structures such as the Approachable Free Subset Property. In the first
talk, I will discuss these principles and their relations, and present new
results from a joint work with Dominik Adolf concerning their consistency
and consistency strength. The second talk will focus on the extender-based
Prikry forcing and its connection with these principles.
(KGRC) research seminar talk on Thursday, April 22
Kurt Godel Research Center
4/19/2021 13:21:37
Research seminar
Kurt Gödel Research Center
Thursday, April 22
"MAD families and strategically bounding forcings"
Osvaldo Guzmán
(Universidad Nacional Autónoma de México)
The notion of strategically bounding forcings is a natural game-theoretic
strengthening of the bounding property for partial orders. In this talk, we
will study the basic properties of strategically bounding forcings and talk
about indestructibility of MAD families. The motivation for this work is the
problem of Roitman.
Time and Place
Talk at 3:00pm via Zoom: This talk will be given via Zoom. If you have not
received the meeting link by the day before the talk, please contact
richard.springer@univie.ac.at!
This Week in Logic at CUNY
This Week in Logic at CUNY
4/18/2021 21:51:16
This Week in Logic at CUNY:
- - - - Monday, Apr 19, 2021 - - - -
Logic and Metaphysics Workshop
Date: Monday, April 19th, 4.15-6.15 (NY time)
V. Alexis Peluce (CUNY)
Title: Brouwer’s First Act of Intuitionism
Abstract: L.E.J. Brouwer famously argued that mathematics was completely separated from formal language. His explanation for why this is so leaves room for interpretation. Indeed, one might ask: what sort of philosophical background is required to make sense of the strong anti-linguistic views of Brouwer? In this talk, we outline some possible answers to the above. We then present an interpretation that we argue best makes sense of Brouwer’s first act.
- - - - Tuesday, Apr 20, 2021 - - - -
Models of Peano Arithmetic (MOPA)
Tuesday, April 20, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. Andrés Cordón Franco Universidad de Sevilla
Induction and collection up to definable elements: calibrating the strength of parameter-free ΔnΔn-minimization.
In this talk we shall deal with fragments of first-order Peano Arithmetic obtained by restricting the conclusion of the induction or the collection axiom to elements in a prescribed subclass DD of the universe. Fix n>0n>0. The schemes of ΣnΣn-induction up to ΣmΣm-definable elements and the schemes of ΣnΣn-collection up to ΣmΣm-definable elements form two families of subtheories of IΣnIΣn and BΣnBΣn, respectively, obtained in this way.
The properties of ΣnΣn-induction up to ΣmΣm-definable elements for n≥mn≥m are reasonably well understood and interesting applications of these fragments are known. However, an analysis of the case n<mn<m was pending. In the first part of this talk, we address this problem and show that it is related to the following general question: 'Under which conditions on a model MM can we prove that every non-empty ΣmΣm-definable subset of MM contains some ΣmΣm-definable element?'
In the second part of the talk, we show that, for each n≥1n≥1, the scheme of ΣnΣn-collection up to ΣnΣn-definable elements provides us with an axiomatization of the Σn+1Σn+1-consequences of BΣnBΣn. As an application, we obtain that BΣnBΣn is Σn+1Σn+1-conservative over parameter-free ΔnΔn-minimization (plus IΣn−1IΣn−1), thus partially answering a question of R. Kaye.
This is joint work with F.Félix Lara-Martín (University of Seville).
- - - - Wednesday, Apr 21, 2021 - - - -
- - - - Thursday, Apr 22, 2021 - - - -
Philog SeminarThursday, April 22, 2021, 6:30 PMTodd Stambaugh (John Jay)Knowledge, behavior, and rationality: Rationalizability in epistemic gamesAbstract: In strategic situations, agents base actions on knowledge and beliefs. This includes knowledge about others’ strategies and preferences over strategy profiles, but also about other external factors. Bernheim and Pearce in 1984 independently defined the game theoretic solution concept of rationalizability, which is built on the premise that rational agents will only take actions that are the best response to some situation that they consider possible. This accounts for other agents’ rationality as well, limiting the strategies to which a particular agent must respond, enabling further elimination until the strategies stabilize. We seek to generalize rationalizability to account not only for actions, but knowledge of the world as well. This will enable us to examine the interplay between action based and knowledge based rationality. We give an account of what it means for an action to be rational relative to a particular state of affairs, and in turn relative to a state of knowledge. We present a class of games, Epistemic Messaging Games (EMG), with a communication stage that clarifies the epistemic state among the players prior to the players’ actions. We use a history based model, which frames individual knowledge in terms of local projections of a global history. With this framework, we give an account of rationalizability for subclasses of EMG(Joint work with Rohit Parikh. Todd Stambaugh received his doctorate in 2018, from the mathematics program of CUNY).A Zoom link will be posted on philog.arthurpaulpedersen.org on Wednesday
- - - - Friday, Apr 23, 2021 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, Apr 23, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. Andrés Villaveces, Universidad Nacional de Colombia – Bogotá
Two logics, and their connections with large cardinals / Questions for BDGM: Part II
In the past couple of years I have been involved (joint work with Väänänen and independently with Shelah) with some logics in the vicinity of Shelah's L1κLκ1 (a logic from 2012 that has Interpolation and a very weak notion of compactness, namely Strong Undefinability of Well-Orderings, and in some cases has a Lindström-type theorem for those two properties). Our work with Väänänen weakens the logic but keeps several properties. Our work with Shelah explores the connection with definability of AECs.
These logics seem to have additional interesting properties under the further assumption of strong compactness of a cardinal, and this brings them close to recent work of Boney, Dimopoulos, Gitman and Magidor [BDGM].
During the first lecture, I plan to describe two games and a syntax of two logics: Shelah's L1κLκ1 and my own logic (joint work with Väänänen) L1,cκLκ1,c. I will stress some of the properties of these logics, without any use of large cardinal assumptions.
During the second lecture, I plan to enter rather uncharted territory. I will describe some constructions done by Shelah (mostly) under the assumption of strong compactness, but I also plan to bring these logics to a territory closer to the work of [BDGM]. This second lecture will have more conjectures, ideas, and (hopefully interesting) discussions with some of the authors of that paper.
Next Week in Logic at CUNY:
- - - - Monday, Apr 26, 2021 - - - -
Logic and Metaphysics Workshop
Date: Monday, April 26th, 4.15-6.15 (NY time)
Rohan French (UC Davis).
Title: Non-Classical Metatheory
Abstract: A common line of thinking has it that proponents of non-classical logics who claim that their preferred logic L gives the correct account of validity, while at the same time giving proofs of theorems about L using classical logic, are in some sense being insincere in their claim that L is the correct logic. This line of thought quite naturally motivates a correctness requirement on a non-classical logic L: that it be able to provide internally acceptable proofs of its main metatheorems. Of central importance amongst such metatheorems will typically be soundness and completeness results, such results being apt to play important roles in arguments showing that a given logic gives the correct account of validity. On the face of it this sounds like a reasonable requirement, but determining its precise content requires us to settle two important conceptual questions: what counts as a completeness proof for a logic, and what does it mean for a result to be internally acceptable? To get clearer on this issue we will look at three different results which have some claim to being internally acceptable soundness and completeness proofs, focusing for ease of comparison on the case of intuitionistic propositional logic, examining the extent to which they can be said to provide internally acceptable soundness and completeness results.
- - - - Tuesday, Apr 27, 2021 - - - -
Models of Peano Arithmetic (MOPA)
Tuesday, April 20, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. Dave Marker, University of Illinois at Chicago
Real closures of ω1ω1-like models of PA
D'Aquino, Knight and Starchenko showed the real closure of a model of Peano Arithmetic is recursively saturated. Thus any two countable models of PA with the same standard system have isomorphic real closures. Charlie Steinhorn, Jim Schmerl and I showed that even for ω1ω1-like model of PA the situation is very different. We construct 2ℵ12ℵ1 recursively saturated elementarily equivalent ω1ω1-like models of PA with the same standard system and non-isomorphic real closures.
- - - - Wednesday, Apr 28, 2021 - - - -
- - - - Thursday, Apr 29, 2021 - - - -
- - - - Friday, Apr 30, 2021 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, Apr 30, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. Elliot Glazer, Harvard University
- - - - Other Logic News - - - -
- - - - Web Site - - - -"Find us on the web at: nylogic.github.io(site designed, built & maintained by Victoria Gitman)"-------- ADMINISTRIVIA --------To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.
Barcelona Set theory Seminar
Barcelona Logic Seminar
4/18/2021 12:10:49
Dear All,
Please find attached the announcement of the next session of the Barcelona Set Theory Seminar. Feel free to distribute it.
SPEAKER: Sam Roberts (Universität Konstanz)
TITLE: Reinhardt’s potentialism
DATE: 21 April 2021
TIME: 16:00 (CEST)
PLACE: The Seminar will take place online at the following address:
Best regards,
Joan
P.S.: If you do not wish to receive any more announcements, please send an email to
bagaria@ub.edu with the text “Unsubscribe”.
Joan Bagaria
ICREA Research Professor
Universitat de Barcelona
Departament de Matemàtiques i Informàtica
Gran Via de les Corts Catalanes 585
08007 Barcelona
Catalonia
Phone: +34 93 402 1609
Tomorrow talk by Micheal Hrusak (1:30 pm Toronto time)
Toronto Set Theory Seminar
4/15/2021 11:00:00
Hello everyone,
Please
use the following link and fill the form (every week) to enter the
meeting. This form helps the Field Institute to know statistical data
about attendance.
Here the speaker information:
Date and Time: Friday, April 16th, 2021 - 1:30pm to 3:00pm
Title:
Ultrafiters, MAD families and the Kat\v{e}tov order
Abstract:
We shall survey recent results concerning classification of MAD
families and ultrafilters using the Kat\v{e}tov order, concentrating on
open problems.
Iván Ongay Valverde (he/his)
Friday 16th talk by Micheal Hrusak (1:30 pm Toronto time)
Toronto Set Theory Seminar
4/13/2021 0:51:40
Hello everyone,
Please
use the following link and fill the form (every week) to enter the
meeting. This form helps the Field Institute to know statistical data
about attendance.
Here the speaker information:
Date and Time: Friday, April 16th, 2021 - 1:30pm to 3:00pm
Title:
Ultrafiters, MAD families and the Kat\v{e}tov order
Abstract:
We shall survey recent results concerning classification of MAD
families and ultrafilters using the Kat\v{e}tov order, concentrating on
open problems.
Iván Ongay Valverde (he/his)
(KGRC) research seminar talk on Thursday, April 15
Kurt Godel Research Center
4/12/2021 12:47:17
Research seminar
Kurt Gödel Research Center
Thursday, April 15
"Choice, Groups, and Topoi"
Andreas Blass (University of Michigan)
Work of Tarski, Mostowski, Gauntt, and Truss provides finite,
group-theoretic criteria for ZF-provability of implications between weak
choice axioms of the form "every family of n-element sets has a choice
function" or "every countable family of n-element sets has a choice
function." From a sufficiently broad, category-theoretic viewpoint, these
implications and the equivalent group-theoretic criteria look like exactly
the same statements but interpreted in different categories, namely
certain particular sorts of topoi. The main result is that this
equivalence applies not only to these particular sorts of topoi but to all
topoi. I plan to describe the ingredients of this work --- choice
principles, group properties, and topoi --- and, if time permits, give a
hint about the ideas in the proofs.
Time and Place
Talk at 3:00pm via Zoom: This talk will be given via Zoom. If you have not
received the meeting link by the day before the talk, please contact
richard.springer@univie.ac.at!
Two talks on Tuesday, April 20
Carnegie Mellon Logic Seminar
4/12/2021 10:27:26
TUESDAY, April 20, 2021
Mathematical logic seminar: 3:30 P.M., Online, Sandra Müller, University
of Vienna
Join Zoom Meeting: https://cmu.zoom.us/j/621951121 [cmu.zoom.us]
Meeting ID: 621 951 121
TITLE: Large cardinals and determinacy when all sets are universally Baire
ABSTRACT: The large cardinal strength of the Axiom of Determinacy when
enhanced with the hypothesis that all sets of reals are universally Baire
is known to be much stronger than the Axiom of Determinacy itself. In
fact, Sargsyan conjectured it to be as strong as the existence of a
cardinal that is both a limit of Woodin cardinals and a limit of strong
cardinals. Larson, Sargsyan and Wilson showed that this would be optimal
via a generalization of Woodin's derived model construction. After a
gentle introduction to the connection between determinacy axioms and large
cardinals we will sketch a proof of Sargsyan's conjecture.
TUESDAY, April 20, 2021
Set Theory Reading Group: 4:30 P.M., Online, Sandra Müller, University of
Vienna
Join Zoom Meeting: https://cmu.zoom.us/j/621951121 [cmu.zoom.us]
Meeting ID: 621 951 121
TITLE: The exact consistency strength of "AD + all sets are universally
Baire"
ABSTRACT: In this second talk, we will outline the proof of Sargsyan's
conjecture with more details. In particular, we will discuss a new
translation procedure for hybrid mice extending work of Steel, Zhu and
Sargsyan that is crucial in the construction of a model with a cardinal
that is both a limit of Woodin cardinals and a limit of strong cardinals
from a model of the Axiom of Determinacy in which all sets of reals are
universally Baire.
UPDATE: This Week in Logic at CUNY
This Week in Logic at CUNY
4/12/2021 9:24:01
Hi everyone,
Additional details have been added for this Thursday's talk by Joe Halpern in the Philog Seminar.
Best,
Jonas
This Week in Logic at CUNY:
- - - - Monday, Apr 12, 2021 - - - -
Logic and Metaphysics Workshop
Date: Monday, April 12th, 4.15-6.15 (NY time)
William Nava (NYU)
Title: Logical deducibility and substitution in Bolzano (and beyond)
Abstract: Bolzano is famously responsible for an influential substitutional account of logical consequence (or, as he calls it, logical deducibility): a proposition, 𝜑, is logically deducible from a set of propositions, Γ, iff every uniform substitution of non-logical ideas in Γ∪{𝜑} that makes every proposition in Γ true also makes 𝜑 true. There are two problems with making sense of Bolzano’s proposal, however. One is that Bolzano argues that every proposition is of the form a has B—in other words, is a monadic atomic predication. So, for Bolzano, logically complex propositions like ‘𝜑 and 𝜓’ cannot have the semantic structure they appear to. This can be addressed, roughly, by taking complex propositions to predicate logical ideas of collections of propositions. But this introduces the second problem: for Bolzano, familiar logical ideas like ‘and’, ‘or’, and ‘not’ are complex ideas with compositional structure. I’ll show that, as a result of this structure, we cannot use the simple and familiar notion of uniform substitution in order to understand logical deducibility. We must instead use what I’ll call form-sensitive substitution. I will end by drawing some general lessons about substitutional definitions of logical consequence in languages with the resources to generate complex predicates of propositions.
- - - - Tuesday, Apr 13, 2021 - - - -
Models of Peano Arithmetic (MOPA)
Tuesday, April 13, 7pm
The seminar will take place virtually at 7pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. Roman Kossak, CUNY
Automorphisms, Jónsson Models, and Satisfaction Classes
25 years ago I wrote a paper on four open problems concerning recursively saturated models of PA. The problems are still open. I will talk about two of them: (1) Let M be a countable recursively saturated model of PA. Can every automorphism of M be extended to some recursively saturated elementary end extension of M? (2) Is there a recursively saturated model of PA that has no recursively saturated elementary submodel of the same cardinality as the model? I will present some partial results involving partial inductive satisfaction classes.
- - - - Wednesday, Apr 14, 2021 - - - -
- - - - Thursday, Apr 15, 2021 - - - -
Philog Seminar
Thursday, April 15, 6:30 PM
Joe Halpern, Cornell University
Actual Causality: A Survey
What does it mean that an event C ``actually caused'' event E?
The problem of defining actual causation goes beyond mere philosophical
speculation. For example, in many legal arguments, it is precisely what
needs to be established in order to determine responsibility. (What exactly
was the actual cause of the car accident or the medical problem?)
The philosophy literature has been struggling with the problem
of defining causality since the days of Hume, in the 1700s.
Many of the definitions have been couched in terms of counterfactuals.
(C is a cause of E if, had C not happened, then E would not have happened.)
In 2001, Judea Pearl and I introduced a new definition of actual cause,
using Pearl's notion of structural equations to model
counterfactuals. The definition has been revised twice since then,
extended to deal with notions like "responsibility" and "blame", and
applied in databases and program verification. I survey
the last 15 years of work here, including joint work
with Judea Pearl, Hana Chockler, and Chris Hitchcock. The talk will be
completely self-contained.
A Zoom link will be posted on April 14 on
https://philog.arthurpaulpedersen.org/
- - - - Friday, Apr 16, 2021 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, Apr 16, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. Andrés Villaveces CUNY
Next Week in Logic at CUNY:
- - - - Monday, Apr 19, 2021 - - - -
Logic and Metaphysics Workshop
Date: Monday, April 19th, 4.15-6.15 (NY time)
V. Alexis Peluce (CUNY)
Title: Brouwer’s First Act of Intuitionism
Abstract: L.E.J. Brouwer famously argued that mathematics was completely separated from formal language. His explanation for why this is so leaves room for interpretation. Indeed, one might ask: what sort of philosophical background is required to make sense of the strong anti-linguistic views of Brouwer? In this talk, we outline some possible answers to the above. We then present an interpretation that we argue best makes sense of Brouwer’s first act.
- - - - Tuesday, Apr 20, 2021 - - - -
Models of Peano Arithmetic (MOPA)
Tuesday, April 20, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. Andrés Cordón Franco Universidad de Sevilla
- - - - Wednesday, Apr 21, 2021 - - - -
- - - - Thursday, Apr 22, 2021 - - - -
- - - - Friday, Apr 23, 2021 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, Apr 23, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. Andrés Villaveces CUNY
- - - - Other Logic News - - - -
- - - - Web Site - - - -"Find us on the web at: nylogic.github.io(site designed, built & maintained by Victoria Gitman)"-------- ADMINISTRIVIA --------To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.
Logic Seminar 14 April 2021 17:00 hrs by Karen Seidel, HPI, University of Potsdam
NUS Logic Seminar
4/12/2021 8:25:07
Invitation to the Logic Seminar at the National University of Singapore
Date: Wednesday, 14 April 2020, 17:00 hrs
Talk via Zoom: https://nus-sg.zoom.us/j/96860201432?pwd=cVdwZmd2clVFaEhaTmJjaGdXMFdmdz09
Meeting ID: 968 6020 1432
Password: Is P=NP?
Speaker: Karen Seidel
Title: Learning from informant
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Abstract:
Learning from positive and negative information, so called informant,
is one of the models for human and machine learning introduced by Gold.
We review existing classical and recent results regarding the learning
power of associated settings.
Barcelona Set theory Seminar
Barcelona Logic Seminar
4/12/2021 3:00:44
Dear All,
Please find attached the announcement of the next session of the Barcelona Set Theory Seminar. Feel free to distribute it.
SPEAKER: Erin Carmody (Fordham University)
TITLE: The relationships between measurable and strongly compact cardinals
DATE: 14 April 2021
TIME: 16:00 (CEST)
PLACE: The Seminar will take place online at the following address:
Best regards,
Joan
P.S.: If you do not wish to receive any more announcements, please send an email to
bagaria@ub.edu with the text “Unsubscribe”.
Joan Bagaria
ICREA Research Professor
Universitat de Barcelona
Departament de Matemàtiques i Informàtica
Gran Via de les Corts Catalanes 585
08007 Barcelona
Catalonia
Phone: +34 93 402 1609
This Week in Logic at CUNY
This Week in Logic at CUNY
4/11/2021 22:00:00
This Week in Logic at CUNY:
- - - - Monday, Apr 12, 2021 - - - -
Logic and Metaphysics Workshop
Date: Monday, April 12th, 4.15-6.15 (NY time)
William Nava (NYU)
Title: Logical deducibility and substitution in Bolzano (and beyond)
Abstract: Bolzano is famously responsible for an influential substitutional account of logical consequence (or, as he calls it, logical deducibility): a proposition, 𝜑, is logically deducible from a set of propositions, Γ, iff every uniform substitution of non-logical ideas in Γ∪{𝜑} that makes every proposition in Γ true also makes 𝜑 true. There are two problems with making sense of Bolzano’s proposal, however. One is that Bolzano argues that every proposition is of the form a has B—in other words, is a monadic atomic predication. So, for Bolzano, logically complex propositions like ‘𝜑 and 𝜓’ cannot have the semantic structure they appear to. This can be addressed, roughly, by taking complex propositions to predicate logical ideas of collections of propositions. But this introduces the second problem: for Bolzano, familiar logical ideas like ‘and’, ‘or’, and ‘not’ are complex ideas with compositional structure. I’ll show that, as a result of this structure, we cannot use the simple and familiar notion of uniform substitution in order to understand logical deducibility. We must instead use what I’ll call form-sensitive substitution. I will end by drawing some general lessons about substitutional definitions of logical consequence in languages with the resources to generate complex predicates of propositions.
- - - - Tuesday, Apr 13, 2021 - - - -
Models of Peano Arithmetic (MOPA)
Tuesday, April 13, 7pm
The seminar will take place virtually at 7pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. Roman Kossak, CUNY
Automorphisms, Jónsson Models, and Satisfaction Classes
25 years ago I wrote a paper on four open problems concerning recursively saturated models of PA. The problems are still open. I will talk about two of them: (1) Let M be a countable recursively saturated model of PA. Can every automorphism of M be extended to some recursively saturated elementary end extension of M? (2) Is there a recursively saturated model of PA that has no recursively saturated elementary submodel of the same cardinality as the model? I will present some partial results involving partial inductive satisfaction classes.
- - - - Wednesday, Apr 14, 2021 - - - -
- - - - Thursday, Apr 15, 2021 - - - -
Philog Seminar
Thursday, April 8, 6:30 PM
Speaker: Joseph Halpern, Cornell
- - - - Friday, Apr 16, 2021 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, Apr 16, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. Andrés Villaveces CUNY
Next Week in Logic at CUNY:
- - - - Monday, Apr 19, 2021 - - - -
Logic and Metaphysics Workshop
Date: Monday, April 19th, 4.15-6.15 (NY time)
V. Alexis Peluce (CUNY)
Title: Brouwer’s First Act of Intuitionism
Abstract: L.E.J. Brouwer famously argued that mathematics was completely separated from formal language. His explanation for why this is so leaves room for interpretation. Indeed, one might ask: what sort of philosophical background is required to make sense of the strong anti-linguistic views of Brouwer? In this talk, we outline some possible answers to the above. We then present an interpretation that we argue best makes sense of Brouwer’s first act.
- - - - Tuesday, Apr 20, 2021 - - - -
Models of Peano Arithmetic (MOPA)
Tuesday, April 20, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. Andrés Cordón Franco Universidad de Sevilla
- - - - Wednesday, Apr 21, 2021 - - - -
- - - - Thursday, Apr 22, 2021 - - - -
- - - - Friday, Apr 23, 2021 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, Apr 23, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. Andrés Villaveces CUNY
- - - - Other Logic News - - - -
- - - - Web Site - - - -"Find us on the web at: nylogic.github.io(site designed, built & maintained by Victoria Gitman)"-------- ADMINISTRIVIA --------To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.
Unusual time for tomorrow talk by Joerg Brendle (10:30 am Toronto time)
Toronto Set Theory Seminar
4/8/2021 14:42:50
Hello everyone,
Please remember that Toronto just had a daylight saving change of time and please notice the UNUSUAL TIME.
Please
use the following link and fill the form (every week) to enter the
meeting. This form helps the Field Institute to know statistical data
about attendance.
Here the speaker information:
Date and Time: Friday, April 9th, 2021 - 10:30am to 12:00pm
Title:
Combinatorics of ultrafilters on complete Boolean algebras
Abstract:
The combinatorial structure of ultrafilters on the natural numbers has been investigated intensively for many decades, and a lot is known about the order structure of such ultrafilters (under either the Tukey or the Rudin-Keisler ordering), about special classes of ultrafilters (like P-points),or about cardinal invariants related to ultrafilters (like the ultrafilter number). Yet, very little has beendone so far concerning combinatorial aspects of ultrafilters on general Boolean algebras, and thepurpose of this talk will be to present some basic results in this direction.
Focus will be put on the Tukey ordering, on (non)existence of non-Tukey-maximal ultrafilters, on ultrafilter numbers, and on an analogue of the Rudin-Keisler ordering in the context of complete Boolean algebras. We will in particular deal with Cohen and random algebras. This is joint work with Francesco Parente.
Iván Ongay Valverde (he/his)
Unusual time for Friday 9th talk by Joerg Brendle (10:30 am Toronto time)
Toronto Set Theory Seminar
4/5/2021 12:41:43
Hello everyone,
Please remember that Toronto just had a daylight saving change of time and please notice the UNUSUAL TIME.
Please
use the following link and fill the form (every week) to enter the
meeting. This form helps the Field Institute to know statistical data
about attendance.
Here the speaker information:
Date and Time: Friday, April 9th, 2021 - 10:30am to 12:00pm
Title:
Combinatorics of ultrafilters on complete Boolean algebras
Abstract:
The combinatorial structure of ultrafilters on the natural numbers has been investigated intensively for many decades, and a lot is known about the order structure of such ultrafilters (under either the Tukey or the Rudin-Keisler ordering), about special classes of ultrafilters (like P-points),or about cardinal invariants related to ultrafilters (like the ultrafilter number). Yet, very little has beendone so far concerning combinatorial aspects of ultrafilters on general Boolean algebras, and thepurpose of this talk will be to present some basic results in this direction.
Focus will be put on the Tukey ordering, on (non)existence of non-Tukey-maximal ultrafilters, on ultrafilter numbers, and on an analogue of the Rudin-Keisler ordering in the context of complete Boolean algebras. We will in particular deal with Cohen and random algebras. This is joint work with Francesco Parente.
Best
Iván Ongay Valverde (he/his)
This Week in Logic at CUNY
This Week in Logic at CUNY
4/5/2021 11:03:19
This Week in Logic at CUNY:
- - - - Monday, Apr 5, 2021 - - - -
Logic and Metaphysics Workshop
Spring 2021
Date: Monday, April 5th, 4.15-6.15 (NY time)
For meeting information, please email: yweiss@gradcenter.cuny.edu Speakers: Federico Pailos and Eduardo Barrio (Buenos Aires)
Title: A Metainferential Solution to the Adoption Problem
Abstract: In ‘The Question of Logic’ (Kripke 2020) and “The Adoption Problem and the Epistemology of Logic” (Padró 2020), Kripke and Padró argue against the possibility of adopting an alternative logic. Without having already endorsed a logic, it is not possible to derive the consequences of an alternative system. In particular, without Modus Ponens in the metatheory, one could not adopt any inferential rule at all. This seems to cause trouble for logics like LP, that does not validate this rule. Modus Ponens is a self-governing rule that cannot be adopted and could not be rejected. This is connected with the problem of the tortoise reasoner (Scambler 2019) and the problem of the tortoise Logic (Priest 2021). In this talk, we offer a new solution. With the metainferential logic TS/LP it is possible to model metalogical Modus Ponens-like reasoning while still rejecting Modus Ponens.
- - - - Tuesday, Apr 6, 2021 - - - -
Models of Peano Arithmetic (MOPA)
Tuesday, April 6, 7pm
The seminar will take place virtually at 7pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. Zachiri McKenzie
Topless powerset preserving end-extensions and rank-extensions of countable models of set theory
This talk will report on ongoing work that is being done in collaboration with Ali Enayat (University of Gothenburg).
For models of set theory NN and MM, NN is a powerset preserving end-extension of MM if NN is an end-extension of MM and NN contains no new subsets of sets in MM. A model of Kripke-Platek Set Theory, NN, is a rank-extension of a model of Kripke-Platek Set Theory, MM, if NN is an end-extension of MM and all of the new sets in NN have rank that exceeds the rank of all of the sets in MM. A powerset preserving end-extension (rank-extension) NN of MM is topless if M≠NM≠N and there is no set in N∖MN∖M containing only sets from MM. If M=⟨M,EM⟩M=⟨M,EM⟩ is a model of set theory, then the admissible cover of MM, CovMCovM, is defined to be the smallest admissible structure with MM forming its urelements and whose language contains a unary function function symbol, FF, that sends each m∈Mm∈M to the set {x∈M∣xEMm}{x∈M∣xEMm}. Barwise has shown that if MM is a model of Kripke-Platek Set Theory, then CovMCovM exists and its minimality facilitates compactness arguments for infinitary languages coded in CovMCovM. We extend Barwise's analysis by showing that if MM satisfies enough set theory then the expansion of CovMCovM obtained by adding the powerset function remains admissible. This allows us to build powerset preserving end-extensions and rank-extensions of countable models of certain subsystems of ZFCZFC satisfying any given recursive subtheory of the model being extended. In particular, we show that
- Every countable model of KPPKPP has a topless rank-extension that satisfies KPPKPP.
- Every countable ωω-standard model of MOST+Π1-collectionMOST+Π1-collection has a topless powerset preserving end-extension that satisfies MOST+Π1-collectionMOST+Π1-collection.
- - - - Wednesday, Apr 7, 2021 - - - -
- - - - Thursday, Apr 8, 2021 - - - -
Philog Seminar
Thursday, April 8, 6:30 PM
Speaker: Jongjin (JJ) Kim (Korea University)
Abstract. We discuss two approaches to life: presentism and futurism. We locate presentism within various elements of Buddhism, in the form of advice to live in the present and not to allow the future to hinder us from living in the ever present now. By contrast, futurism, which we identify with Karl Popper, advises us to think of future consequences before we act, and to act now for a better future. Of course, with its emphasis on a well-defined path to an ideal future ideally culminating in enlightenment, Buddhism undoubtedly has elements of futurism as well. We do not intend to determine which of these two approaches to time is more dominant in Buddhism, nor how the two approaches are best understood within Buddhism; but simply we intend to compare and contrast these two approaches, using those presentist elements of Buddhism as representative of presentism while contrasting them with those elements of futurism to be found in Popper and others. We will discuss various aspects of presentism and futurism, such as Ruth Millikan’s Popperian animal, the psychologist Howard Rachlin’s social and temporal discounting, and even the popular but controversial idea, YOLO (you only live once). The primary purpose of this paper is to contrast one with the other. The central question of ethics is: How should one live? Our variation on that question is: When should one live? We conjecture that the notion of flow, developed by Csikszentmihalyi, may be a better optimal choice between these two positions.
Jongjin Kim received his doctorate in Philosophy from CUNY in 2019.
For Zoom link please go to
https://philog.arthurpaulpedersen.org/on Wednesday
- - - - Friday, Apr 9, 2021 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, Apr 9, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. Sandra Müller, University of Vienna
The exact consistency strength of 'AD + all sets are universally Baire'
The large cardinal strength of the Axiom of Determinacy when enhanced with the hypothesis that all sets of reals are universally Baire is known to be much stronger than the Axiom of Determinacy itself. In fact, Sargsyan conjectured it to be as strong as the existence of a cardinal that is both a limit of Woodin cardinals and a limit of strong cardinals. Larson, Sargsyan and Wilson showed that this would be optimal via a generalization of Woodin’s derived model construction. We will discuss a new translation procedure for hybrid mice extending work of Steel, Zhu and Sargsyan and use this to prove Sargsyan’s conjecture.
Next Week in Logic at CUNY:
- - - - Monday, Apr 12, 2021 - - - -
Logic and Metaphysics Workshop
Date: Monday, April 5th, 4.15-6.15 (NY time)
William Nava (NYU)
Title: Logical deducibility and substitution in Bolzano (and beyond)
Abstract: Bolzano is famously responsible for an influential substitutional account of logical consequence (or, as he calls it, logical deducibility): a proposition, 𝜑, is logically deducible from a set of propositions, Γ, iff every uniform substitution of non-logical ideas in Γ∪{𝜑} that makes every proposition in Γ true also makes 𝜑 true. There are two problems with making sense of Bolzano’s proposal, however. One is that Bolzano argues that every proposition is of the form a has B—in other words, is a monadic atomic predication. So, for Bolzano, logically complex propositions like ‘𝜑 and 𝜓’ cannot have the semantic structure they appear to. This can be addressed, roughly, by taking complex propositions to predicate logical ideas of collections of propositions. But this introduces the second problem: for Bolzano, familiar logical ideas like ‘and’, ‘or’, and ‘not’ are complex ideas with compositional structure. I’ll show that, as a result of this structure, we cannot use the simple and familiar notion of uniform substitution in order to understand logical deducibility. We must instead use what I’ll call form-sensitive substitution. I will end by drawing some general lessons about substitutional definitions of logical consequence in languages with the resources to generate complex predicates of propositions.
- - - - Tuesday, Apr 13, 2021 - - - -
Models of Peano Arithmetic (MOPA)
Tuesday, April 13, 7pm
The seminar will take place virtually at 7pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. Roman Kossak, CUNY
Automorphisms, Jónsson Models, and Satisfaction Classes
25 years ago I wrote a paper on four open problems concerning recursively saturated models of PA. The problems are still open. I will talk about two of them: (1) Let M be a countable recursively saturated model of PA. Can every automorphism of M be extended to some recursively saturated elementary end extension of M? (2) Is there a recursively saturated model of PA that has no recursively saturated elementary submodel of the same cardinality as the model? I will present some partial results involving partial inductive satisfaction classes.
- - - - Wednesday, Apr 14, 2021 - - - -
- - - - Thursday, Apr 15, 2021 - - - -
- - - - Friday, Apr 16, 2021 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, Apr 16, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. Andrés Villaveces CUNY
- - - - Other Logic News - - - -Conference announcement: Boise Extravaganza in Set Theory (BEST) June 17-20
The 2021 Boise Extravaganza in Set Theory will take place in Zoomland during June 17-20. We would be delighted if you will attend! (Please follow
https://www.boisestate.edu/math/best for future updates.)
We are currently welcoming applications to speak at BEST from researchers in set theory and related fields. We hope to receive your application by May 1, but we will continue accepting applications as long as there is space. To apply please send your name, institution, career status (and if student, advisor name), talk title, and abstract to
best@boisestate.edu.
- - - - Web Site - - - -"Find us on the web at: nylogic.github.io(site designed, built & maintained by Victoria Gitman)"-------- ADMINISTRIVIA --------To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.
Barcelona Set theory Seminar
Barcelona Logic Seminar
4/4/2021 17:51:22
Dear All,
Please find attached the announcement of the next session of the Barcelona Set Theory Seminar. Feel free to distribute it.
SPEAKER: Farmer Schlutzenberg (Muenster)
TITLE: Some results on restricted mantles
DATE: 7 April 2021
TIME: 16:00 (CET)
PLACE: The Seminar will take place online at the following address:
Best regards,
Joan
P.S.: If you do not wish to receive any more announcements, please send an email to
bagaria@ub.edu with the text “Unsubscribe”.
Joan Bagaria
ICREA Research Professor
Universitat de Barcelona
Departament de Matemàtiques i Informàtica
Gran Via de les Corts Catalanes 585
08007 Barcelona
Catalonia
Phone: +34 93 402 1609
Logic Seminar 7 April 2021 17:00 hrs at NUS by Frank Stephan
NUS Logic Seminar
4/4/2021 5:03:09
Invitation to the Logic Seminar at the National University of Singapore
Date: Wednesday, 7 April 2020, 17:00 hrs
Talk via Zoom: https://nus-sg.zoom.us/j/96860201432?pwd=cVdwZmd2clVFaEhaTmJjaGdXMFdmdz09
Meeting ID: 968 6020 1432
Password: Is P=NP?
Speaker: Frank Stephan
Title: On Trees without Hyperimmune Branches
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
In the year 2013, Keng Meng Ng, Frank Stephan, Yue Yang and Liang Yu
published the paper "Computational Aspects of the Hyperimmune-free Degrees"
and one of the results was given without a proof. The current talk gives
the full proof of this result. In particular, the talk provides
the full details of the construction of an co-r.e.\ infinite binary tree
with uncountablly many branches which are all hyperimmune-free,
Schnorr-trivial, jump traceable, generalised low and of minimal
Turing degree. Hyperimmune-free means that every function Turing
reducible to it is majorised by a recursive function. Jump traceable
means that for every e one can compute an explicit bound on the
number of elements which some further set also depending on e enumerates
and that finite set contains the Jump value at e. Generalised low means
that the jump of A is recursive in the join of A and K. A minimal
Turing degree is a nonrecursive Turing degree below which is only
the recursive one. Schnorr trivial means that for every f truth-table
reducible to the set there is a recursive function which lists out for
each input x a set of x+1 many values with one of them being f(x).
The slides of the quite technical talk are here:
http://www.comp.nus.edu.sg/~fstephan/hiftree2021slides.ps ,
http://www.comp.nus.edu.sg/~fstephan/hiftree2021slides.pdf .
As at least two of the authors of the paper are regular participants
of the logic seminar, this is also an opportunity to present to them
the full details of the proof.
Logic Seminar Tomorrow in Singapore
NUS Logic Seminar
3/29/2021 21:47:05
Hello, this is a reminder on tomorrow's logic seminar. I also
attach the handout of the speaker for the logic seminar (the date
is 31 March 2021, 17:00 hrs Singapore time = 11:00 hrs Central
European Summer Time). The handout is also linked to the logic
seminar entry for the talk. See you then. Best regards, Frank
Invitation to the Logic Seminar at the National University of Singapore
Date: Wednesday, 31 March 2021, 17:00 hrs
Talk via Zoom: https://nus-sg.zoom.us/j/96860201432?pwd=cVdwZmd2clVFaEhaTmJjaGdXMFdmdz09
Meeting ID: 968 6020 1432
Password: Is P=NP?
Speaker: Lars Kristiansen, University of Oslo
Title: Classic representations of irrational numbers seen from a computability
and complexity-theoretic perspective.
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Abstract:
We will address the following question:
Do we need, or do we not need, unbounded search in order to convert
one representation of an irrational number into another
representation?
We will consider well known representations like Cauchy sequences,
Dedekind cuts, base-2 expansions, base-10 expansions and continued
fractions, and maybe a few less well-know representations.
Logic Seminar Wednesday 31 March 2021
NUS Logic Seminar
3/29/2021 0:27:38
Invitation to the Logic Seminar at the National University of Singapore
Date: Wednesday, 31 March 2021, 17:00 hrs
Talk via Zoom: https://nus-sg.zoom.us/j/96860201432?pwd=cVdwZmd2clVFaEhaTmJjaGdXMFdmdz09
Meeting ID: 968 6020 1432
Password: Is P=NP?
Speaker: Lars Kristiansen, University of Oslo
Title: Classic representations of irrational numbers seen from a computability
and complexity-theoretic perspective.
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Abstract:
We will address the following question:
Do we need, or do we not need, unbounded search in order to convert
one representation of an irrational number into another
representation?
We will consider well known representations like Cauchy sequences,
Dedekind cuts, base-2 expansions, base-10 expansions and continued
fractions, and maybe a few less well-know representations.
This Week in Logic at CUNY
This Week in Logic at CUNY
3/28/2021 20:59:35
This Week in Logic at CUNY:
- - - - Monday, Mar 29, 2021 - - - -
- - - - Tuesday, Mar 30, 2021 - - - -
Models of Peano Arithmetic (MOPA)
Tuesday, Mar 30, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. Paola d’Aquino, Università della Campania -“L. Vanvitelli”
Residue rings of models of Peano Arithmetic
I will present an axiomatization of a class of residue rings of models of PA. This is obtained using valuation theory and results on models of PA. (Joint work with A. Macintyre)
- - - - Wednesday, Mar 31, 2021 - - - -
- - - - Thursday, Apr 1, 2021 - - - -
- - - - Friday, Apr 2, 2021 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, Apr 2, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. Monroe Eskew University of Vienna
The approximation property and generic embeddings
The approximation property was introduced by Hamkins for his Gap Forcing Theorem, and it has turned out to be a very useful notion, appearing for example in the partial equiconsistency result of Viale and Weiss on PFA, and in the proof of Woodin's HOD Dichotomy Theorem. In the context of generic embeddings, there can be a useful interplay between elementarity and approximation. We discuss some recent work in this direction: (1) tensions between saturated ideals on ω2ω2 and the tree property (with Sean Cox), (2) fragility of the strong independence spectra (with Vera Fischer), and (3) mutual inconsistency of Foreman‘s minimal generic hugeness axioms.
Next Week in Logic at CUNY:
- - - - Monday, Apr 5, 2021 - - - -
- - - - Tuesday, Apr 6, 2021 - - - -
Models of Peano Arithmetic (MOPA)
Tuesday, April 6, 7pm
The seminar will take place virtually at 7pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. Zachiri McKenzie
TBA
- - - - Wednesday, Apr 7, 2021 - - - -
- - - - Thursday, Apr 8, 2021 - - - -
- - - - Friday, Apr 9, 2021 - - - -
- - - - Other Logic News - - - -Conference announcement: Boise Extravaganza in Set Theory (BEST) June 17-20
The 2021 Boise Extravaganza in Set Theory will take place in Zoomland during June 17-20. We would be delighted if you will attend! (Please follow
https://www.boisestate.edu/math/best for future updates.)
We are currently welcoming applications to speak at BEST from researchers in set theory and related fields. We hope to receive your application by May 1, but we will continue accepting applications as long as there is space. To apply please send your name, institution, career status (and if student, advisor name), talk title, and abstract to
best@boisestate.edu.
- - - - Web Site - - - -"Find us on the web at: nylogic.github.io(site designed, built & maintained by Victoria Gitman)"-------- ADMINISTRIVIA --------To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.
Unusual time for tomorrow talk by Sakaé Fuchino (10:30 am Toronto time)
Toronto Set Theory Seminar
3/25/2021 10:00:00
Hello everyone,
Please remember that Toronto just had a daylight saving change of time and please notice the UNUSUAL TIME.
Please
use the following link and fill the form (every week) to enter the
meeting. This form helps the Field Institute to know statistical data
about attendance.
Here the speaker information:
Date and Time: Friday, March 26th, 2021 - 10:30am to 12:00pm
Title: Laver-generically large cardinal and the Continuum Problem
Abstract:
Let us call a class $\calP$ of posets iterable, if, for any $\poP\in\calP$ and $\calP$-name
$\utpoQ$\vspace{-0.5\smallskipamount} \st\ $\forces{\poP}{\utpoQ\in\calP}$, we have
$\poP\ast\utpoQ\in\calP$.
For an iterable class $\mathcal{P}$ of posets, a cardinal $\mu$ is called {\it Laver-generically
supercompact for $\mathcal{P}$}, if, for any $\mathbb{P}\in\mathcal{P}$ and $\lambda\in\On$,
there is a $\poP$-name $\utpoQ$\vspace{-0.5\smallskipamount} with $\forces{\poP}{\utpoQ\in\calP}$ \st, letting
$\poQ=\poP\ast\utpoQ$,
there are $j$, $M\subseteq\uniV[\genH]$ for $(\uniV, \mathbb{Q})$-generic
$\genH$ such that
1) $\elembed{j}{V}{M}$,\smallskip
2) $crit(j)=\mu$, $j(\mu)>\lambda$,\smallskip
3) $\cardof{\poQ}\leq j(\mu)$,\smallskip
4) $\poP$, $\genH\in M$ and \smallskip
5) $j\imageof\lambda\in M$.\\\\
The notion of Laver-generically superhugeness is obtained when \assert{5} is replaced by
5') $j\imageof j(\mu)\in M$.
The notion of Laver-generically large cardinal for $\calP$ given here is stronger than the one
introduced in \cite{II} and is called there the {\it strongly} and {\it tightly}
Laver-generically large cardinal (the strongness corresponds the usage of two-step
iteration in the definition instead of just $\poP\circleq\poQ$, and the tightness the
condition \assert{3}).
In my talk, I will give a proof of the following:\quad
For many natural iterable class of proper posets $\mathcal{P}$, a
Laver-generically supercompact cardinal $\mu$ for $\poP$ is either $\aleph_2$ or very large (if it
exists),
and the continuum is either $\aleph_1$ or $\aleph_2$, or $\geq\mu$ in case of very large
$\mu$, where it depends on $P$ which scenario we have.
If time allows, I will also sketch a proof of the following theorem:\quad
If $\mathcal{P}$ is the class of c.c.c.\ posets (or some other iterable class $\calP$ of posets preserving all
cardinalities but adding some real), and if $\mu$ is Laver-generically superhuge for $\mathcal{P}$, then
$\mu=2^{\aleph_0}$.
At the moment, it is open if the same theorem holds for a Laver-generically supercompact
Iván Ongay Valverde (he/his)
(KGRC) research seminar talk on Thursday, March 25
Kurt Godel Research Center
3/22/2021 13:09:53
Research seminar
Kurt Gödel Research Center
Thursday, March 25
"Splitting Localization and prediction numbers"
Iván Ongay-Valverde (York University, Canada)
In 1993, Newelski and Roslanowski studied some cardinal characteristics related
to the unsymmetric game (I, as Geschke, called them the localization numbers).
While doing this, they found the n-localization property. When a forcing has
this property, you can ensure that all new reals are 'tame' somehow (for
example, you do not add Cohen or Random reals).
In a different line of study, Andreas Blass worked with some cardinal
characteristics related to the idea of guessing correctly a real number given
certain amount of information (he called them evasion and prediction numbers).
In 2010, it was an open question whether some possible variations of these
numbers were known cardinal characteristics or not.
Impressively, these two notions are related.
In this talk, we will show that the k global adaptive prediction numbers are
not any other cardinal characteristic. In particular, they are not the
localization numbers. To do this, we will use techniques analogue to Newelski
and Roslanowski and we will show that the n-localization can be weakened to get
their result.
Time and Place
Talk at 3:00pm via Zoom: This talk will be given via Zoom. If you have not
received the meeting link by the day before the talk, please contact
richard.springer@univie.ac.at!
* * *
Please note: There will be no talks in the KGRC research seminar on April 1 and
April 8 due to the Easter break in Austria.
This Week in Logic at CUNY
This Week in Logic at CUNY
3/21/2021 22:56:21
This Week in Logic at CUNY:
- - - - Monday, Mar 15, 2021 - - - -
Logic and Metaphysics Workshop
Date: Monday, Mar 15, 4.15-6.15 (NY time)
Speaker: Eric Bayruns Garcia (Cal State San Bernardino)
Title: Belief Content and Rationality: Why Racist Beliefs Are Not Rational
Abstract: I present a novel defense of the evidentialist thesis in the debate between epistemologists who defend this thesis and those who defend the moral encroachment thesis. Both sides of the moral encroachment-evidentialism debate suppose that the belief class of what I call seemingly-rational-racist beliefs obtains. I reject that this belief class of seemingly- rational-racist beliefs obtains on the basis that beliefs with this kind of content are false and evidentially unsupported. I submit that they are false and evidentially unsupported because of how the content of these beliefs relate to the social-linguistic practices and habits that compose racial injustice in the US and other similarly colonized societies. I diagnose that a problem with this debate is that both sides in this debate conceive of the content of race terms and beliefs that attribute negative features to Black, Indigenous and Latinx persons without considering how they function in a racially unjust society.
- - - - Tuesday, Mar 16, 2021 - - - -Models of Peano Arithmetic (MOPA)
Tuesday, Mar 9, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. Mateusz Łełyk, University of Warsaw
TBA
- - - - Wednesday, Mar 17, 2021 - - - -The New York City Category Theory Seminar
Speaker: Tobias Fritz, University of Innsbruck.
Date and Time: Wednesday March 17, 2021, 7:00 - 8:30 PM., on Zoom.
Title: Categorical Probability and the de Finetti Theorem.
Abstract: I will give an introduction to categorical probability in terms of Markov categories, followed by a discussion of the classical de Finetti theorem within that framework. Depending on whether current ideas work out or not, I may (or may not) also present a sketch of a purely categorical proof of the de Finetti theorem based on the law of large numbers. Joint work with Tomáš Gonda, Paolo Perrone and Eigil Fjeldgren Rischel.
- - - - Thursday, Mar 18, 2021 - - - -- - - - Friday, Mar 19, 2021 - - - -Set Theory Seminar
CUNY Graduate Center
Friday, Mar 19, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. Paul Blain Levy, University of Birmingham
Broad Infinity and Generation Principles
Broad Infinity is a new and arguably intuitive axiom scheme in set theory. It states that 'broad numbers', which are three-dimensional trees whose growth is controlled, form a set. If the Axiom of Choice is assumed, then Broad Infinity is equivalent to the Ord-is-Mahlo scheme: every closed unbounded class of ordinals contains a regular ordinal.
Whereas the axiom of Infinity leads to generation principles for sets and families and ordinals, Broad Infinity leads to more advanced versions of these principles. The talk explains these principles and how they are related under various prior assumptions: the Axiom of Choice, the Law of Excluded Middle, and weaker assumptions.
Next Week in Logic at CUNY:- - - - Monday, Mar 22, 2021 - - - -Logic and Metaphysics WorkshopDate: Monday, Mar 1, 4.15-6.15 (NY time)Martin Pleitz (Münster).
Title: Dualism about Generality
Abstract: In my talk I will motivate, outline, and apply a variant of first order predicate logic that can distinguish between two kinds of generality, which I call objectual generality and conceptual generality. To see the difference, compare the two general statements ‘Every human is a featherless biped’ and ‘Every human is a rational animal’. On a charitable understanding, the first sentence is about all humans past and present, as a subcollection of all particular objects currently accessible to us, while the second sentence is not about any particular object at all, but about the interaction of the concepts of being human and being a rational animal. Historically, the quantified sentences of predicate logic have been understood in either of the two ways. Frege understood them as expressing conceptual generalities; hence it was natural for him to call his predicate logic a “Concept Script”. Today, they are usually understood as objectual generalities, manifest both in the idea that a quantified sentence is like a conjunction (or disjunction) of its instances and in the current model theoretic orientation in semantics. But as we can find ourselves in a situation where we want to talk about both kinds of generality (and their interaction), it is worthwhile to develop the resources to express them within a single system. I will outline such a system that results from adding a second pair of quantifiers to regular first order predicate logic, and sketch applications to the notion of analyticity, natural kind predicates, and an ontological argument.
- - - - Tuesday, Mar 23, 2021 - - - -Models of Peano Arithmetic (MOPA)
Tuesday, Mar 23, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. Mateusz Łełyk, University of Warsaw
Nonequivalent axiomatizations of PA and the Tarski Boundary: Part III
This is a continuation of the talk from Feb 16th. This time we shall study different theories of the form CT−[δ]CT−[δ] which are conservative extensions of a PAPA. In particular, we prove the following theorem.
Theorem 2 There exists a family {δf}f∈ω∗{δf}f∈ω∗ such that for all f,g∈ω∗f,g∈ω∗
1) CT−[δf]CT−[δf] is conservative over PAPA;
2) if f⊊gf⊊g, then CT−[δg]CT−[δg] properly extends CT−[δf]CT−[δf];
3) if f⊥gf⊥g then CT−[δg]∪CT−[δf]CT−[δg]∪CT−[δf] is nonconservative over PAPA (but consistent).
We will finish the proof of the theorem announced in the abstract of part II.
- - - - Wednesday, Mar 24, 2021 - - - -- - - - Thursday, Mar 25, 2021 - - - -Philog Seminar
6:30 PM, Thursday, March 25
Rohit Parikh (CUNY) on
The Logic of Knowledge Based Obligation (joint work with Eric Pacuit (UMD) and Eva Cogan (Brooklyn))
Our obligations depend on what we know. If we do not know that we need to do X then there is no obligation to actually do X. However, sometimes there is also an obligation to know and hence also an obligation to inform. We look into the temporal logic of such issues, relying on work by John Horty and by Parikh and Ramanujam.
- - - - Friday, Mar 26, 2021 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, Mar 26, 11am
The seminar will take place virtually at 11am US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. Carolin Antos, University of Konstanz
The 'algebraic' vs. 'non-algebraic' distinction: New impulses for the universe/multiverse debate?
The distinction between 'algebraic' and 'non-algebraic fields in mathematics, coined by Shapiro (1997), plays an important role in discussions about the status of set theory and connects back to the so-called universe/multiverse debate in the philosophy of set theory. In this talk we will see, that this distinction is not as clear cut as is usually assume when using it in the debate. In particular, we will see that in more recent formulations of this distinction, multiversism seems to split into a a strong and a weaker form. This can be translated to a meta-level, when considering the background theory in which set-theoretic multiversism can take place. This offers a more fine-grained picture of multiversism and allows us to mitigate a standard universist objection based on the conception of a multiversist background theory.
Next Week in Logic at CUNY:
- - - - Monday, Mar 29, 2021 - - - -
- - - - Tuesday, Mar 30, 2021 - - - -
Models of Peano Arithmetic (MOPA)
Tuesday, Mar 30, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. Paola d’Aquino, Università della Campania -“L. Vanvitelli”
TBA
- - - - Wednesday, Mar 31, 2021 - - - -
- - - - Thursday, Apr 1, 2021 - - - -
- - - - Friday, Apr 2, 2021 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, Apr 2, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. Monroe Eskew University of Vienna
TBA
- - - - Other Logic News - - - -Conference announcement: Boise Extravaganza in Set Theory (BEST) June 17-20
The 2021 Boise Extravaganza in Set Theory will take place in Zoomland during June 17-20. We would be delighted if you will attend! (Please follow
https://www.boisestate.edu/math/best for future updates.)
We are currently welcoming applications to speak at BEST from researchers in set theory and related fields. We hope to receive your application by May 1, but we will continue accepting applications as long as there is space. To apply please send your name, institution, career status (and if student, advisor name), talk title, and abstract to
best@boisestate.edu.
- - - - Web Site - - - -"Find us on the web at: nylogic.github.io(site designed, built & maintained by Victoria Gitman)"-------- ADMINISTRIVIA --------To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.
UPDATE: This Week in Logic at CUNY
This Week in Logic at CUNY
3/21/2021 22:58:43
I removed the previous week's events from the calendar this time - sorry for any confusion.
Best,
Jonas
This Week in Logic at CUNY:
- - - - Monday, Mar 22, 2021 - - - -Logic and Metaphysics WorkshopDate: Monday, Mar 1, 4.15-6.15 (NY time)Martin Pleitz (Münster).
Title: Dualism about Generality
Abstract: In my talk I will motivate, outline, and apply a variant of first order predicate logic that can distinguish between two kinds of generality, which I call objectual generality and conceptual generality. To see the difference, compare the two general statements ‘Every human is a featherless biped’ and ‘Every human is a rational animal’. On a charitable understanding, the first sentence is about all humans past and present, as a subcollection of all particular objects currently accessible to us, while the second sentence is not about any particular object at all, but about the interaction of the concepts of being human and being a rational animal. Historically, the quantified sentences of predicate logic have been understood in either of the two ways. Frege understood them as expressing conceptual generalities; hence it was natural for him to call his predicate logic a “Concept Script”. Today, they are usually understood as objectual generalities, manifest both in the idea that a quantified sentence is like a conjunction (or disjunction) of its instances and in the current model theoretic orientation in semantics. But as we can find ourselves in a situation where we want to talk about both kinds of generality (and their interaction), it is worthwhile to develop the resources to express them within a single system. I will outline such a system that results from adding a second pair of quantifiers to regular first order predicate logic, and sketch applications to the notion of analyticity, natural kind predicates, and an ontological argument.
- - - - Tuesday, Mar 23, 2021 - - - -Models of Peano Arithmetic (MOPA)
Tuesday, Mar 23, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. Mateusz Łełyk, University of Warsaw
Nonequivalent axiomatizations of PA and the Tarski Boundary: Part III
This is a continuation of the talk from Feb 16th. This time we shall study different theories of the form CT−[δ]CT−[δ] which are conservative extensions of a PAPA. In particular, we prove the following theorem.
Theorem 2 There exists a family {δf}f∈ω∗{δf}f∈ω∗ such that for all f,g∈ω∗f,g∈ω∗
1) CT−[δf]CT−[δf] is conservative over PAPA;
2) if f⊊gf⊊g, then CT−[δg]CT−[δg] properly extends CT−[δf]CT−[δf];
3) if f⊥gf⊥g then CT−[δg]∪CT−[δf]CT−[δg]∪CT−[δf] is nonconservative over PAPA (but consistent).
We will finish the proof of the theorem announced in the abstract of part II.
- - - - Wednesday, Mar 24, 2021 - - - -- - - - Thursday, Mar 25, 2021 - - - -Philog Seminar
6:30 PM, Thursday, March 25
Rohit Parikh (CUNY) on
The Logic of Knowledge Based Obligation (joint work with Eric Pacuit (UMD) and Eva Cogan (Brooklyn))
Our obligations depend on what we know. If we do not know that we need to do X then there is no obligation to actually do X. However, sometimes there is also an obligation to know and hence also an obligation to inform. We look into the temporal logic of such issues, relying on work by John Horty and by Parikh and Ramanujam.
- - - - Friday, Mar 26, 2021 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, Mar 26, 11am
The seminar will take place virtually at 11am US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. Carolin Antos, University of Konstanz
The 'algebraic' vs. 'non-algebraic' distinction: New impulses for the universe/multiverse debate?
The distinction between 'algebraic' and 'non-algebraic fields in mathematics, coined by Shapiro (1997), plays an important role in discussions about the status of set theory and connects back to the so-called universe/multiverse debate in the philosophy of set theory. In this talk we will see, that this distinction is not as clear cut as is usually assume when using it in the debate. In particular, we will see that in more recent formulations of this distinction, multiversism seems to split into a a strong and a weaker form. This can be translated to a meta-level, when considering the background theory in which set-theoretic multiversism can take place. This offers a more fine-grained picture of multiversism and allows us to mitigate a standard universist objection based on the conception of a multiversist background theory.
Next Week in Logic at CUNY:
- - - - Monday, Mar 29, 2021 - - - -
- - - - Tuesday, Mar 30, 2021 - - - -
Models of Peano Arithmetic (MOPA)
Tuesday, Mar 30, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. Paola d’Aquino, Università della Campania -“L. Vanvitelli”
TBA
- - - - Wednesday, Mar 31, 2021 - - - -
- - - - Thursday, Apr 1, 2021 - - - -
- - - - Friday, Apr 2, 2021 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, Apr 2, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. Monroe Eskew University of Vienna
TBA
- - - - Other Logic News - - - -Conference announcement: Boise Extravaganza in Set Theory (BEST) June 17-20
The 2021 Boise Extravaganza in Set Theory will take place in Zoomland during June 17-20. We would be delighted if you will attend! (Please follow
https://www.boisestate.edu/math/best for future updates.)
We are currently welcoming applications to speak at BEST from researchers in set theory and related fields. We hope to receive your application by May 1, but we will continue accepting applications as long as there is space. To apply please send your name, institution, career status (and if student, advisor name), talk title, and abstract to
best@boisestate.edu.
- - - - Web Site - - - -"Find us on the web at: nylogic.github.io(site designed, built & maintained by Victoria Gitman)"-------- ADMINISTRIVIA --------To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.
Barcelona Set theory Seminar
Barcelona Logic Seminar
3/21/2021 13:21:20
Dear All,
Please find attached the announcement of the next session of the Barcelona Set Theory Seminar. Feel free to distribute it.
SPEAKER: Peter Koellner (Harvard University)
TITLE: Minimal models and $\beta$-categoricity
DATE: 24 March 2021
TIME: 16:00 (CET)
PLACE: The Seminar will take place online at the following address:
Best regards,
Joan
P.S.: If you do not wish to receive any more announcements, please send an email to
bagaria@ub.edu with the text “Unsubscribe”.
Joan Bagaria
ICREA Research Professor
Universitat de Barcelona
Departament de Matemàtiques i Informàtica
Gran Via de les Corts Catalanes 585
08007 Barcelona
Catalonia
Phone: +34 93 402 1609
Unusual time for Friday 26th talk by Sakae Fuchino (10:30 am)
Toronto Set Theory Seminar
3/20/2021 10:00:00
Hello everyone,
Please remember that Toronto just had a daylight saving change of time and please notice the UNUSUAL TIME.
Please
use the following link and fill the form (every week) to enter the
meeting. This form helps the Field Institute to know statistical data
about attendance.
Here the speaker information:
Date and Time: Friday, March 26th, 2021 - 10:30am to 12:00pm
Title: Laver-generically large cardinal and the Continuum Problem
Abstract:
Let us call a class $\calP$ of posets iterable, if, for any $\poP\in\calP$ and $\calP$-name
$\utpoQ$\vspace{-0.5\smallskipamount} \st\ $\forces{\poP}{\utpoQ\in\calP}$, we have
$\poP\ast\utpoQ\in\calP$.
For an iterable class $\mathcal{P}$ of posets, a cardinal $\mu$ is called {\it Laver-generically
supercompact for $\mathcal{P}$}, if, for any $\mathbb{P}\in\mathcal{P}$ and $\lambda\in\On$,
there is a $\poP$-name $\utpoQ$\vspace{-0.5\smallskipamount} with $\forces{\poP}{\utpoQ\in\calP}$ \st, letting
$\poQ=\poP\ast\utpoQ$,
there are $j$, $M\subseteq\uniV[\genH]$ for $(\uniV, \mathbb{Q})$-generic
$\genH$ such that
1) $\elembed{j}{V}{M}$,\smallskip
2) $crit(j)=\mu$, $j(\mu)>\lambda$,\smallskip
3) $\cardof{\poQ}\leq j(\mu)$,\smallskip
4) $\poP$, $\genH\in M$ and \smallskip
5) $j\imageof\lambda\in M$.\\\\
The notion of Laver-generically superhugeness is obtained when \assert{5} is replaced by
5') $j\imageof j(\mu)\in M$.
The notion of Laver-generically large cardinal for $\calP$ given here is stronger than the one
introduced in \cite{II} and is called there the {\it strongly} and {\it tightly}
Laver-generically large cardinal (the strongness corresponds the usage of two-step
iteration in the definition instead of just $\poP\circleq\poQ$, and the tightness the
condition \assert{3}).
In my talk, I will give a proof of the following:\quad
For many natural iterable class of proper posets $\mathcal{P}$, a
Laver-generically supercompact cardinal $\mu$ for $\poP$ is either $\aleph_2$ or very large (if it
exists),
and the continuum is either $\aleph_1$ or $\aleph_2$, or $\geq\mu$ in case of very large
$\mu$, where it depends on $P$ which scenario we have.
If time allows, I will also sketch a proof of the following theorem:\quad
If $\mathcal{P}$ is the class of c.c.c.\ posets (or some other iterable class $\calP$ of posets preserving all
cardinalities but adding some real), and if $\mu$ is Laver-generically superhuge for $\mathcal{P}$, then
$\mu=2^{\aleph_0}$.
At the moment, it is open if the same theorem holds for a Laver-generically supercompact
Iván Ongay Valverde (he/his)
Talk tomorrow by Anush Tserunyan (1 30 pm in new daylight saving time)
Toronto Set Theory Seminar
3/18/2021 12:00:00
Hello everyone,
Please remember that Toronto just had a daylight saving change of time.
Please use the following link and fill the form (every week) to enter the meeting. This form helps the Field Institute to know statistical data about attendance.
Here the speaker information:
Date and Time: Friday, March 19th, 2021 - 1:30pm to 3:00pm
Title: Ergodic theorems along treesAbstract:
In the classical pointwise ergodic theorem for a probability measure preserving (pmp) transformation $T$, one takes averages of a given integrable function over the intervals $\{x, T(x), T^2(x), \hdots, T^n(x)\}$ in the forward orbit of the point $x$. In joint work with Jenna Zomback, we prove a “backward” ergodic theorem for a countable-to-one pmp $T$, where the averages are taken over subtrees of the graph of $T$ that are rooted at $x$ and lie behind $x$ (in the direction of $T^{-1}$). Surprisingly, this theorem yields (forward) ergodic theorems for countable groups, in particular, one for pmp actions of free groups of finite rank where the averages are taken along subtrees of the standard Cayley graph rooted at the identity. For free group actions, this strengthens the best known result in this vein due to Bufetov (2000).
Two CMU seminars on Tuesday, March 23
Carnegie Mellon Logic Seminar
3/18/2021 10:05:32
TUESDAY, March 23, 2021
Mathematical logic seminar: 3:30 P.M., Online, Gabriel Goldberg,
University of California, Berkeley
Join Zoom Meeting: https://cmu.zoom.us/j/621951121 [cmu.zoom.us]
Meeting ID: 621 951 121
TITLE: Ordinal definability and the structure of large cardinals, part 1
ABSTRACT: Roughly speaking, Woodin's HOD conjecture asserts that assuming
the existence of very large cardinals, arbitrary sets can be closely
approximated by definable ones. This talk outlines an approach to the
conjecture based on an analysis of the uniqueness properties of
ultrafilters and elementary embeddings, which has a number of
applications: for example, a proof of a variant of the HOD conjecture for
sets definable from ultrafilters, a proof of Woodin's HOD dichotomy
theorem from a single strongly compact cardinal, and a proof that past an
extendible cardinal, elementary embeddings of the universe of sets are
uniquely determined by their codomains.
TUESDAY, March 23, 2021
Set Theory Reading Group: 4:30 P.M., Online, Gabriel Goldberg, University
of California, Berkeley
Join Zoom Meeting: https://cmu.zoom.us/j/621951121 [cmu.zoom.us]
Meeting ID: 621 951 121
TITLE: Ordinal definability and the structure of large cardinals, part 2
ABSTRACT: Roughly speaking, Woodin's HOD conjecture asserts that assuming
the existence of very large cardinals, arbitrary sets can be closely
approximated by definable ones. This talk outlines an approach to the
conjecture based on an analysis of the uniqueness properties of
ultrafilters and elementary embeddings, which has a number of
applications: for example, a proof of a variant of the HOD conjecture for
sets definable from ultrafilters, a proof of Woodin's HOD dichotomy
theorem from a single strongly compact cardinal, and a proof that past an
extendible cardinal, elementary embeddings of the universe of sets are
uniquely determined by their codomains.
Reminder of talk today at 10:00 hrs
NUS Logic Seminar
3/17/2021 20:07:53
Hello, this is a reminder for Liling Ko's talk today at 10:00 hrs
using the usual logic seminar login. It is the same as for next
talk which I send in the subsequent email. Best regards, Frank
Logic Seminar 24 March 2021 17:00 hrs at NUS by Philipp Schlicht
NUS Logic Seminar
3/17/2021 20:10:47
Invitation to the Logic Seminar at the National University of Singapore
Date: Wednesday, 24 Marc 2020, 17:00 hrs
Talk via Zoom: https://nus-sg.zoom.us/j/96860201432?pwd=cVdwZmd2clVFaEhaTmJjaGdXMFdmdz09
Meeting ID: 968 6020 1432
Password: Is P=NP?
Speaker: Philipp Schlicht
Title: Sets and graphs in generalised descriptive set theory
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Abstract: While descriptive set theory studies definable sets of words of
length omega, generalised descriptive set theory studies words
of uncountable regular length. The talk will begin with an
introduction to this field and its applications. I will then talk
about how one can characterise when a definable set is small
or admits a colouring with few colours with respect to an open
graph.
This is joint work with Dorottya Sziraki.
(KGRC) research seminar talk on Thursday, March 18
Kurt Godel Research Center
3/15/2021 12:08:38
Research seminar
Kurt Gödel Research Center
Thursday, March 18
"Partition forcing"
Jaroslav Šupina
(Pavol Jozef Šafárik University in Košice, Slovakia)
A. Miller introduced in 1980 a forcing notion we refer to as a partition
forcing. Although it is a variant of Sacks' perfect set forcing, it is closely
related to Miller's rational perfect set forcing.
The talk is devoted to our application of partition forcing in a proof of
consistency of $\mathfrak{u}=\mathfrak{i}<\mathfrak{a}_T$. Here, $\mathfrak{i}$
is the minimal cardinality of a maximal independent family, $\mathfrak{u}$ a
minimal size of an ultrafilter base, and $\mathfrak{a}_T$ is the minimal
cardinality of a maximal family of pairwise almost disjoint subtrees of
$2^{<\omega}$.
This is a joint work with Vera Fischer.
Time and Place
Talk at 3:00pm via Zoom: This talk will be given via Zoom. If you have not
received the meeting link by the day before the talk, please contact
richard.springer@univie.ac.at!
Barcelona Set theory Seminar
Barcelona Logic Seminar
3/15/2021 4:27:42
Dear All,
Please find attached the announcement of the next session of the Barcelona Set Theory Seminar. Feel free to distribute it.
SPEAKER: Wojciech
Woloszyn (University of Oxford)
TITLE: Modal graph theory as a
foundation of mathematics
DATE: 17 March 2021
TIME: 16:00 (CET)
PLACE: The Seminar will take place online at the following address:
Best regards,
Joan
P.S.: If you do not wish to receive any more announcements, please send an email to
bagaria@ub.edu with the text “Unsubscribe”.
Joan Bagaria
ICREA Research Professor
Universitat de Barcelona
Departament de Matemàtiques i Informàtica
Gran Via de les Corts Catalanes 585
08007 Barcelona
Catalonia
Phone: +34 93 402 1609
This Friday talk by Anush Tserunyan (1 30 pm in new daylight saving time)
Toronto Set Theory Seminar
3/14/2021 23:50:58
Hello everyone,
Today we had a time change in Toronto. Please check how does it differ from your time zone to avoid missing the seminar.
Please use the following link and fill the form (every week) to enter the meeting. This form helps the Field Institute to know statistical data about attendance.
Here the speaker information:
Date and Time: Friday, March 19th, 2021 - 1:30pm to 3:00pm
Title: Ergodic theorems along treesAbstract:
In the classical pointwise ergodic theorem for a probability measure preserving (pmp) transformation $T$, one takes averages of a given integrable function over the intervals $\{x, T(x), T^2(x), \hdots, T^n(x)\}$ in the forward orbit of the point $x$. In joint work with Jenna Zomback, we prove a “backward” ergodic theorem for a countable-to-one pmp $T$, where the averages are taken over subtrees of the graph of $T$ that are rooted at $x$ and lie behind $x$ (in the direction of $T^{-1}$). Surprisingly, this theorem yields (forward) ergodic theorems for countable groups, in particular, one for pmp actions of free groups of finite rank where the averages are taken along subtrees of the standard Cayley graph rooted at the identity. For free group actions, this strengthens the best known result in this vein due to Bufetov (2000).
This Week in Logic at CUNY
This Week in Logic at CUNY
3/14/2021 23:46:33
This Week in Logic at CUNY:
- - - - Monday, Mar 15, 2021 - - - -
Logic and Metaphysics Workshop
Date: Monday, Mar 15, 4.15-6.15 (NY time)
Speaker: Eric Bayruns Garcia (Cal State San Bernardino)
Title: Belief Content and Rationality: Why Racist Beliefs Are Not Rational
Abstract: I present a novel defense of the evidentialist thesis in the debate between epistemologists who defend this thesis and those who defend the moral encroachment thesis. Both sides of the moral encroachment-evidentialism debate suppose that the belief class of what I call seemingly-rational-racist beliefs obtains. I reject that this belief class of seemingly- rational-racist beliefs obtains on the basis that beliefs with this kind of content are false and evidentially unsupported. I submit that they are false and evidentially unsupported because of how the content of these beliefs relate to the social-linguistic practices and habits that compose racial injustice in the US and other similarly colonized societies. I diagnose that a problem with this debate is that both sides in this debate conceive of the content of race terms and beliefs that attribute negative features to Black, Indigenous and Latinx persons without considering how they function in a racially unjust society.
- - - - Tuesday, Mar 16, 2021 - - - -Models of Peano Arithmetic (MOPA)
Tuesday, Mar 9, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. Mateusz Łełyk, University of Warsaw
TBA
- - - - Wednesday, Mar 17, 2021 - - - -The New York City Category Theory Seminar
Speaker: Tobias Fritz, University of Innsbruck.
Date and Time: Wednesday March 17, 2021, 7:00 - 8:30 PM., on Zoom.
Title: Categorical Probability and the de Finetti Theorem.
Abstract: I will give an introduction to categorical probability in terms of Markov categories, followed by a discussion of the classical de Finetti theorem within that framework. Depending on whether current ideas work out or not, I may (or may not) also present a sketch of a purely categorical proof of the de Finetti theorem based on the law of large numbers. Joint work with Tomáš Gonda, Paolo Perrone and Eigil Fjeldgren Rischel.
- - - - Thursday, Mar 18, 2021 - - - -- - - - Friday, Mar 19, 2021 - - - -Set Theory Seminar
CUNY Graduate Center
Friday, Mar 19, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. Paul Blain Levy, University of Birmingham
Broad Infinity and Generation Principles
Broad Infinity is a new and arguably intuitive axiom scheme in set theory. It states that 'broad numbers', which are three-dimensional trees whose growth is controlled, form a set. If the Axiom of Choice is assumed, then Broad Infinity is equivalent to the Ord-is-Mahlo scheme: every closed unbounded class of ordinals contains a regular ordinal.
Whereas the axiom of Infinity leads to generation principles for sets and families and ordinals, Broad Infinity leads to more advanced versions of these principles. The talk explains these principles and how they are related under various prior assumptions: the Axiom of Choice, the Law of Excluded Middle, and weaker assumptions.
Next Week in Logic at CUNY:- - - - Monday, Mar 22, 2021 - - - -Logic and Metaphysics WorkshopDate: Monday, Mar 1, 4.15-6.15 (NY time)Martin Pleitz (Münster).
Title: Dualism about Generality
Abstract: In my talk I will motivate, outline, and apply a variant of first order predicate logic that can distinguish between two kinds of generality, which I call objectual generality and conceptual generality. To see the difference, compare the two general statements ‘Every human is a featherless biped’ and ‘Every human is a rational animal’. On a charitable understanding, the first sentence is about all humans past and present, as a subcollection of all particular objects currently accessible to us, while the second sentence is not about any particular object at all, but about the interaction of the concepts of being human and being a rational animal. Historically, the quantified sentences of predicate logic have been understood in either of the two ways. Frege understood them as expressing conceptual generalities; hence it was natural for him to call his predicate logic a “Concept Script”. Today, they are usually understood as objectual generalities, manifest both in the idea that a quantified sentence is like a conjunction (or disjunction) of its instances and in the current model theoretic orientation in semantics. But as we can find ourselves in a situation where we want to talk about both kinds of generality (and their interaction), it is worthwhile to develop the resources to express them within a single system. I will outline such a system that results from adding a second pair of quantifiers to regular first order predicate logic, and sketch applications to the notion of analyticity, natural kind predicates, and an ontological argument.
- - - - Tuesday, Mar 23, 2021 - - - -- - - - Wednesday, Mar 24, 2021 - - - -- - - - Thursday, Mar 25, 2021 - - - -- - - - Friday, Mar 26, 2021 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, Mar 26, 11am
The seminar will take place virtually at 11am US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. Carolin Antos, University of Konstanz
- - - - Other Logic News - - - -- - - - Web Site - - - -"Find us on the web at: nylogic.github.io(site designed, built & maintained by Victoria Gitman)"-------- ADMINISTRIVIA --------To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.
Talk tomorrow by Anush Tserunyan (1 30 pm)
Toronto Set Theory Seminar
3/14/2021 23:33:27
Hello everyone,
Please remember that Toronto just had a daylight saving change of time.
Please use the
following link and fill the form (every week) to enter the meeting. This
form helps the Field Institute to know statistical data about
attendance.
Here the speaker information:
Date and Time: Friday, March 19th, 2021 - 1:30pm to 3:00pm
Title: Ergodic theorems along treesAbstract:
In the classical pointwise ergodic theorem for a probability measure
preserving (pmp) transformation $T$, one takes averages of a given
integrable function over the intervals $\{x, T(x), T^2(x), \hdots,
T^n(x)\}$ in the forward orbit of the point $x$. In joint work with
Jenna Zomback, we prove a “backward” ergodic theorem for a
countable-to-one pmp $T$, where the averages are taken over subtrees of
the graph of $T$ that are rooted at $x$ and lie behind $x$ (in the
direction of $T^{-1}$). Surprisingly, this theorem yields (forward)
ergodic theorems for countable groups, in particular, one for pmp
actions of free groups of finite rank where the averages are taken along
subtrees of the standard Cayley graph rooted at the identity. For free
group actions, this strengthens the best known result in this vein due
to Bufetov (2000).
Iván Ongay Valverde (he/his)
Talk by Anush Tserunyan Friday 19th (1 30 pm)
Toronto Set Theory Seminar
3/13/2021 9:00:00
Hello everyone,
Please use the
following link and fill the form (every week) to enter the meeting. This
form helps the Field Institute to know statistical data about
attendance.
Here the speaker information:
Speaker : Menachem Kojman
Date and Time: Friday, March 19th, 2021 - 1:30pm to 3:00pm
Title:
Ergodic theorems along trees
Abstract:
In the classical pointwise ergodic theorem for a probability measure
preserving (pmp) transformation $T$, one takes averages of a given
integrable function over the intervals $\{x, T(x), T^2(x), \hdots,
T^n(x)\}$ in the forward orbit of the point $x$. In joint work with
Jenna Zomback, we prove a “backward” ergodic theorem for a
countable-to-one pmp $T$, where the averages are taken over subtrees of
the graph of $T$ that are rooted at $x$ and lie behind $x$ (in the
direction of $T^{-1}$). Surprisingly, this theorem yields (forward)
ergodic theorems for countable groups, in particular, one for pmp
actions of free groups of finite rank where the averages are taken along
subtrees of the standard Cayley graph rooted at the identity. For free
group actions, this strengthens the best known result in this vein due
to Bufetov (2000).
Iván Ongay Valverde (he/his)
CMU seminars on Tuesday, March 16
Carnegie Mellon Logic Seminar
3/12/2021 12:14:46
TUESDAY, March 16, 2021
Mathematical logic seminar: 3:30 P.M., Online, Clinton Conley, CMU
Join Zoom Meeting: https://cmu.zoom.us/j/621951121 [cmu.zoom.us]
Meeting ID: 621 951 121
TITLE: Dividing the sphere by rotations, part 1
ABSTRACT: We say that a subset A of the sphere r-divides it if r-many
rotations of A perfectly tile the sphere's surface. Such divisions were
first exhibited by Robinson ('47) and developed by Mycielski ('55). We
discuss a colorful approach to finding these divisions which are Lebesgue
measurable or possess the property of Baire. This includes joint work with
J. Grebik, A. Marks, O. Pikhurko, and S. Unger.
TUESDAY, March 16, 2021
Set Theory Reading Group: 4:30 P.M., Online, Clinton Conley, CMU
Join Zoom Meeting: https://cmu.zoom.us/j/621951121 [cmu.zoom.us]
Meeting ID: 621 951 121
TITLE: Dividing the sphere by rotations, part 2
ABSTRACT: We say that a subset A of the sphere r-divides it if r-many
rotations of A perfectly tile the sphere's surface. Such divisions were
first exhibited by Robinson ('47) and developed by Mycielski ('55). We
discuss a colorful approach to finding these divisions which are Lebesgue
measurable or possess the property of Baire. This includes joint work with
J. Grebik, A. Marks, O. Pikhurko, and S. Unger.
Tomorrow talk by Menachem Kojman (1 30 pm)
Toronto Set Theory Seminar
3/11/2021 13:30:00
Hello everyone,
Please use the
following link and fill the form (every week) to enter the meeting. This
form helps the Field Institute to know statistical data about
attendance.
Here the speaker information:
Speaker : Menachem Kojman
Date and Time: Friday, March 12th, 2021 - 1:30pm to 3:00pm
Title: Strong colorings over partitions
Abstract:
Strong colorings over partitions were introduced last year by Chen-Mertens, Kojman and Steprans.
In the talk I will present the subject and continue to present the next step of the theory, which was developed in a recent joint work by Kojman, Rinot and Steprans.
The advances include stretching arguments which use Walks on Ordinals. I will present this new technique.
Iván Ongay Valverde (he/his)
Boise Extravaganza in Set Theory June 17-20
Conference
3/11/2021
The 2021 Boise Extravaganza in Set Theory will take place in Zoomland during June 17-20. We would be delighted if you will attend! (Please follow https://www.boisestate.edu/math/best for future updates.)
We are currently welcoming applications to speak at BEST from researchers in set theory and related fields. We hope to receive your application by May 1, but we will continue accepting applications as long as there is space. To apply please send your name, institution, career status (and if student, advisor name), talk title, and abstract to best@boisestate.edu.
The BEST conference particularly aims to support the careers of young researchers, so please pass this announcement along to students and colleagues who may not have received it. We strongly encourage persons from groups underrepresented in mathematics to apply.
Plenary speakers:
David Fernández-Bretón (UNAM)
Victoria Gitman (CUNY Graduate Center)
Jun Le Goh (University of Wisconsin)
Lynne Yengulalp (Wake Forest University)
Joseph Zielinski (North Texas)
Additional confirmed speakers
Filippo Calderoni (University of Illinois, Chicago)
Thomas Gilton (University of Pittsburgh)
Osvaldo Guzmán González (UNAM)
Randall Holmes (Boise State University)
Aristotelis Panagiotopoulos (Munster)
Nick Ramsey (UCLA)
Kameryn Williams (Hawaii)
Jenna Zomback (UIUC)
… and more to come!
BEST is an international conference featuring talks on a broad range of recent advances in set theory and related fields of research. The conference is organized by the Set Theory group at Boise State University. Under normal circumstances BEST is supported by NSF, AAAS–Pacific Division, and Boise State University.
Organizers: Liljana Babinkostova, John Clemens, Samuel Coskey, Marion Scheepers
Scientific support: Natasha Dobrinen, Simon Thomas
Tagged: David Fernández-Bretón, Victoria Gitman, Jun Le Goh, Lynne Yengulalp, Joseph Zielinski, Filippo Calderoni, Thomas Gilton, Osvalda Guzmán González, Randall Holmes, Aristotelis Panagiotopoulos, Nick Ramsey, Kameryn Williams, Jenna Zomback
Logic Seminar 18 March 2021 10:00 hrs at NUS by Ko Liling (Notre Dame)
NUS Logic Seminar
3/10/2021 5:34:08
Invitation to the Logic Seminar at the National University of Singapore
Date: Thursday, 18 March 2021, 10:00 hrs
Talk via Zoom: https://nus-sg.zoom.us/j/96860201432?pwd=cVdwZmd2clVFaEhaTmJjaGdXMFdmdz09
Meeting ID: 968 6020 1432
Password: Is P=NP?
Speaker: Ko Liling
Title: Towards finding a lattice of fickleness strictly above omega^2
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Abstract: Given a finite lattice L that can be embedded in the recursively
enumerable (r.e.) Turing degrees (R,<) we do not in
general know how to characterize the degrees d in R below which
L can be bounded. The important characterizations
known so far are of the
L_7 and 1-3-1 lattices, where the former is bounded exactly
by the degrees with fickleness strictly above omega and the
latter is bounded exactly by the degrees containing sets of fickleness
greater equal omega^omega. Given that the
fickleness hierarchy collapses exactly to the powers of omega
with the first few levels being 0,omega,omega^2,...,omega^omega,
we want to find a lattice that characterizes the levels strictly
above omega^2. We begin by exhausting the lattices L that are as
``small'' as L_7 and 1-3-1, but these lattices turn out to
characterize the levels strictly above omega or from omega^omega onwards,
if L is not already embeddable below all non-zero r.e. degrees.
We even considered small infinite lattices but they too behave
like L_7 or 1-3-1. We discovered three lattices besides 1-3-1
that also characterize the levels from omega^omega onwards.
Our search for a candidate characterising the levels
strictly above omega^2 therefore involves the lattice-theoretic
problem of finding lattices that do not contain any of the four
sublattices which characterise the levels from omega^omega onwards
as a sublattice.
Using this criterion as a heuristic we introduce the wide diamond
lattice as a candidate, though we conjecture that this lattice
also behaves like 1-3-1.
Peter Koellner: Minimal Models and β-Categoricity
Bristol Logic and Set Theory Seminar
3/8/2021 12:12:04
Peter Koellner (Harvard) Minimal Models and β-Categoricity
Bristol Logic and Set Theory Seminar
10th March 2021, 4:00 pm – 5:30 pm
Zoom, On-line Please email Sam Adam-Day for the link: me@samadamday.com
-----------------------
Abstract:
Let us say that a theory $T$ in the language of set theory
is \textit{$\beta$-consistent at $\alpha$} if there is a transitive
model of $T$ of height $\alpha$, and let us say that it is
\textit{$\beta$-categorical at $\alpha$} iff there is at most one
transitive model of $T$ of height $\alpha$. Let us also assume, for
ease of formulation, that there are arbitrarily large $\alpha$ such
that $\ZFC$ is $\beta$-consistent at $\alpha$.
The sentence $\VEL$ has the feature that $\ZFC+\VEL$ is
$\beta$-categorical at $\alpha$, for every $\alpha$. If we assume in
addition that $\ZFC+\VEL$ is $\beta$-consistent at $\alpha$, then the
uniquely determined model is $L_\alpha$, and the minimal such model,
$L_{\alpha_0}$, is model of determined by the $\beta$-categorical theory
$\ZFC+\VEL+M$, where $M$ is the statement ``There
does not exist a transitive model of $\ZFC$.''
It is natural to ask whether $\VEL$ is the only sentence that can be
$\beta$-categorical at $\alpha$; that is, whether, there can be a
sentence $\phi$ such that $\ZFC+\phi$ is $\beta$-categorical at
$\alpha$, $\beta$-consistent at $\alpha$, and where the unique model
is not $L_\alpha$. In the early 1970s Harvey Friedman proved a
partial result in this direction. For a given ordinal $\alpha$, let
$n(\alpha)$ be the next admissible ordinal above $\alpha$, and, for
the purposes of this discussion, let us say that an ordinal $\alpha$
is \textit{minimal} iff a bounded subset of $\alpha$ appears in
$L_{n(\alpha)}\setminus L_\alpha$. [Note that $\alpha_0$ is minimal
(indeed a new subset of $\omega$ appears as soon as possible, namely,
in a $\Sigma_1$-definable manner over $L_{\alpha_0+1}$) and an ordinal
$\alpha$ is non-minimal iff $L_{n(\alpha)}$ satisfies that $\alpha$ is
a cardinal.] Friedman showed that for all $\alpha$ which are
non-minimal, $\VEL$ is the only sentence that is $\beta$-categorical
at $\alpha$. The question of whether this is also true for $\alpha$
which are minimal has remained open.
In this talk I will describe some joint work with Hugh Woodin that
bears on this question. In general, when approaching a ``lightface''
question (such as the one under consideration) it is easier to first
address the ``boldface'' analogue of the question by shifting from the
context of $L$ to the context of $L[x]$, where $x$ is a real. In this
new setting everything is relativized to the real $x$: For an ordinal
$\alpha$, we let $n_x(\alpha)$ be the first $x$-admissible ordinal
above $\alpha$, and we say that $\alpha$ is $x$-\textit{minimal} iff a
bounded subset of $\alpha$ appears in
$L_{n_x(\alpha)}[x]\setminus L_{\alpha}[x]$.
\begin{theorem*} Assume $M_1^\#$ exists and is fully iterable. There
is a sentence $\phi$ in the language of set theory with two
additional constants, \r{c} and \r{d}, such that for a Turing cone
of $x$, interpreting \r{c} by $x$, for all $\a$
\begin{enumerate}
\item[(1)] if $L_\alpha[x]\sat\ZFC$ then there is an
interpretation of \r{d} by something in $L_\alpha[x]$ such that
there is a $\beta$-model of $\ZFC+\phi$ of height $\alpha$ and not
equal to $L_\alpha[x]$, and
\item[(2)] if, in addition, $\alpha$ is $x$-minimal, then there is a
\textit{unique} $\beta$-model of $\ZFC+\phi$ of height $\alpha$
and not equal to $L_\alpha[x]$.
\end{enumerate}
\end{theorem*}
The sentence $\phi$ asserts the existence of an object which is
external to $L_\alpha[x]$ and which, in the case where $\alpha$ is
minimal, is canonical. The object is a branch $b$ through a certain
tree in $L_\alpha[x]$, and the construction uses techniques from the
HOD analysis of models of determinacy.
In this talk I will sketch the proof, describe some additional
features of the singleton, and say a few words about why the lightface
version looks difficult.
Tagged: Peter Koellner
(KGRC) research seminar talk on Thursday, March 11
Kurt Godel Research Center
3/8/2021 12:11:04
Research seminar
Kurt Gödel Research Center
Thursday, March 11
The exact consistency strength of "$AD^+$ + all sets are universally Baire"
Sandra Müller (TU Wien and KGRC)
The large cardinal strength of the Axiom of Determinacy when enhanced with
the hypothesis that all sets of reals are universally Baire is known to be
much stronger than the Axiom of Determinacy itself. In fact, Sargsyan
conjectured it to be as strong as the existence of a cardinal that is both
a limit of Woodin cardinals and a limit of strong cardinals. Larson,
Sargsyan and Wilson showed in 2014 that this would be optimal via a
generalization of Woodin's derived model construction. We will discuss a
new translation procedure for hybrid mice extending work of Steel, Zhu and
Sargsyan and use this to prove Sargsyan's conjecture.
Time and Place
Talk at 3:00pm via Zoom: This talk will be given via Zoom. If you have not
received the meeting link by the day before the talk, please contact
richard.springer@univie.ac.at!
Logic Seminar 10 March 2021 17:00 hrs at NUS
NUS Logic Seminar
3/8/2021 4:57:04
Invitation to the Logic Seminar at the National University of Singapore
Date: Wednesday, 10 March 2020, 17:00 hrs
Talk via Zoom: https://nus-sg.zoom.us/j/96860201432?pwd=cVdwZmd2clVFaEhaTmJjaGdXMFdmdz09
Meeting ID: 968 6020 1432
Password: Is P=NP?
Speaker: Zekun Jia
Title: Two Ramsey-theoretic statements in models where AC fails
Abstract: There are a lot of theorems in Ramsey theory whose proof
explicitly or implicitly uses the Axiom of Choice. This talk will
focus on Ramsey's Theorem and Open Ramsey Theorem in three models of
set theory where the Axiom of Choice fails (the basic Cohen model, the
basic Fraenkel model, and the ordered Mostowski model), as well as
some consistency and independence results that follow. Also, the usual
proof of Open Ramsey Theorem on omega given by Galvin and Prikry
assumes the Axiom of Dependent Choice, and this talk will sketch an
improvement on that proof to make it purely constructive.
This project is advised by Zach Norwood.
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Talk by Menachem Kojman this Friday 12th (1 30 pm)
Toronto Set Theory Seminar
3/7/2021 22:19:05
Hello everyone,
Please use the
following link and fill the form (every week) to enter the meeting. This
form helps the Field Institute to know statistical data about
attendance.
Here the speaker information:
Speaker : Menachem Kojman
Date and Time: Friday, March 12th, 2021 - 1:30pm to 3:00pm
Title: Strong colorings over partitions
Abstract:
Strong colorings over partitions were introduced last year by Chen-Mertens, Kojman and Steprans.
In the talk I will present the subject and continue to present the next step of the theory, which was developed in a recent joint work by Kojman, Rinot and Steprans.
The advances include stretching arguments which use Walks on Ordinals. I will present this new technique.
Iván Ongay Valverde (he/his)
Barcelona Set theory Seminar
Barcelona Logic Seminar
3/7/2021 6:45:57
Dear All,
Please find attached the announcement of the next session of the Barcelona Set Theory Seminar. Feel free to distribute it.
SPEAKER: Carolin Antos (University of Konstanz)
TITLE: The “algebraic” vs. “non-algebraic” distinction: New impulses for the universe/multiverse debate?
DATE: 10 March 2021
TIME: 16:00 (CET)
PLACE: The Seminar will take place online at the following address:
Best regards,
Joan
P.S.: If you do not wish to receive any more announcements, please send an email to
bagaria@ub.edu with the text “Unsubscribe”.
Joan Bagaria
ICREA Research Professor
Universitat de Barcelona
Departament de Matemàtiques i Informàtica
Gran Via de les Corts Catalanes 585
08007 Barcelona
Catalonia
Phone: +34 93 402 1609
Upcoming CMU mathematical logic seminars
Carnegie Mellon Logic Seminar
3/5/2021 20:08:23
TUESDAY, March 9, 2021
Mathematical logic seminar: 3:30 P.M., Online, Andrew Swan, CMU
Join Zoom Meeting: https://cmu.zoom.us/j/621951121 [cmu.zoom.us]
Meeting ID: 621 951 121
TITLE: Quotient inductive types without choice
ABSTRACT: Inductive types are types that are freely generated by
collections of algebraic operators. A common example is the collection of
countably branching trees, which is freely generated by two operators: 1)
there is a countably branching tree, which we visualise as the trivial
tree with one node and no branches, and 2) given a countable sequence of
countably branching trees, there is a new countably branching tree, which
we visualise as a root together with a branch for each tree in the
sequence. Quotient inductive types are freely generated by two processes
simultaneously. As well as generating new elements by operators, as for
inductive types, we can also identify two elements together according to a
collection of equations. This is often illustrated with the example of
unordered countably branching trees, where we add equations to the example
above identifying two trees if we can obtain one from the other by
reordering the branches according to a permutation of the naturals.
Inductive types, formalised as W types, are well known to exist in any
elementary topos with natural number object, and in particular the
category of sets under the assumptions of ZF. However, Blass gave an
example of a quotient inductive type that can be constructed in the
category of sets assuming the existence of an uncountable regular
cardinal, but can't probably be constructed in ZF. In between these cases
are classes of quotient inductive types obtained by placing restrictions
on the set of equations that can be explicitly constructed in ZF but
require more elaborate proofs than for W types. I will talk about two such
classes; W types with reductions in presheaves and image preserving
QW-types in sets. The former were developed as a tool in the semantics of
homotopy type theory, giving in particular a version of the small object
argument and a construction of higher inductive types suitable for
categories without exact quotients or infinite colimits. The latter
generalise a construction of hereditarily countable sets due to Jech and
include the famous example of unordered countably branching trees above.
THURSDAY, March 11, 2021
Model Theory Seminar: 10:00 A.M., Online, Adi Jarden, Ariel University
Center of Samaria
Join Zoom Meeting:
https://cmu.zoom.us/j/96301869290?pwd=Qk1zS0h6ZThmUnRpbmNLNkVJSjkrQT09
Meeting ID: 963 0186 9290
Passcode: 567655
TITLE: Uniqueness Triples and the Diamond Principle, Part II
ABSTRACT: We work with a pre-𝜆-frame, which is an abstract elementary
class (AEC) endowed with a collection of basic types and a non-forking
relation satisfying certain natural properties with respect to models of
cardinality 𝜆. We investigate the density of uniqueness triples in a
given pre-𝜆-frames, that is, under what circumstances every basic triple
admits a non-forking extension that is a uniqueness triple. Prior results
in this direction required strong hypotheses on s.
Our main result is an improvement, in that we assume far fewer hypotheses
on s. In particular, we do not require s to satisfy the extension,
uniqueness, stability, or symmetry properties, or any form of local
character, though we do impose the amalgamation and stability properties
in 𝜆+, and we do assume ♢(𝜆+).
As a corollary, by applying our main result to the trivial 𝜆-frame, it
follows that in any AEC K satisfying modest hypotheses on K𝜆 and K𝜆+,
the set of *-domination triples in K𝜆 is dense among the non-algebraic
triples. We also apply our main result to the non-splitting relation,
obtaining the density of uniqueness triples from very few hypotheses.
TUESDAY, March 16, 2021
Mathematical logic seminar: 3:30 P.M., Online, Clinton Conley, CMU
Join Zoom Meeting: https://cmu.zoom.us/j/621951121 [cmu.zoom.us]
Meeting ID: 621 951 121
TITLE: Dividing the sphere by rotations, part 1
ABSTRACT: We say that a subset A of the sphere r-divides it if r-many
rotations of A perfectly tile the sphere's surface. Such divisions were
first exhibited by Robinson ('47) and developed by Mycielski ('55). We
discuss a colorful approach to finding these divisions which are Lebesgue
measurable or possess the property of Baire. This includes joint work
with J. Grebik, A. Marks, O. Pikhurko, and S. Unger.
TUESDAY, March 16, 2021
Set Theory Reading Group: 4:30 P.M., Online, Clinton Conley, CMU
Join Zoom Meeting: https://cmu.zoom.us/j/621951121 [cmu.zoom.us]
Meeting ID: 621 951 121
TITLE: Dividing the sphere by rotations, part 2
ABSTRACT: We say that a subset A of the sphere r-divides it if r-many
rotations of A perfectly tile the sphere's surface. Such divisions were
first exhibited by Robinson ('47) and developed by Mycielski ('55). We
discuss a colorful approach to finding these divisions which are Lebesgue
measurable or possess the property of Baire. This includes joint work
with J. Grebik, A. Marks, O. Pikhurko, and S. Unger.
TUESDAY, March 23, 2021
Mathematical logic seminar: 3:30 P.M., Online, Gabriel Goldberg,
University of California, Berkeley
Join Zoom Meeting: https://cmu.zoom.us/j/621951121 [cmu.zoom.us]
Meeting ID: 621 951 121
TITLE: Ordinal definability and the structure of large cardinals, part 1
ABSTRACT: Roughly speaking, Woodin's HOD conjecture asserts that assuming
the existence of very large cardinals, arbitrary sets can be closely
approximated by definable ones. This talk outlines an approach to the
conjecture based on an analysis of the uniqueness properties of
ultrafilters and elementary embeddings, which has a number of
applications: for example, a proof of a variant of the HOD conjecture for
sets definable from ultrafilters, a proof of Woodin's HOD dichotomy
theorem from a single strongly compact cardinal, and a proof that past an
extendible cardinal, elementary embeddings of the universe of sets are
uniquely determined by their codomains.
TUESDAY, March 23, 2021
Set Theory Reading Group: 4:30 P.M., Online, Gabriel Goldberg, University
of California, Berkeley
Join Zoom Meeting: https://cmu.zoom.us/j/621951121 [cmu.zoom.us]
Meeting ID: 621 951 121
TITLE: Ordinal definability and the structure of large cardinals, part 2
ABSTRACT: Roughly speaking, Woodin's HOD conjecture asserts that assuming
the existence of very large cardinals, arbitrary sets can be closely
approximated by definable ones. This talk outlines an approach to the
conjecture based on an analysis of the uniqueness properties of
ultrafilters and elementary embeddings, which has a number of
applications: for example, a proof of a variant of the HOD conjecture for
sets definable from ultrafilters, a proof of Woodin's HOD dichotomy
theorem from a single strongly compact cardinal, and a proof that past an
extendible cardinal, elementary embeddings of the universe of sets are
uniquely determined by their codomains.
TUESDAY, March 30, 2021
Mathematical logic seminar: 3:30 P.M., Online, Colin Jahel, Université
Claude Bernard Lyon 1
Join Zoom Meeting: https://cmu.zoom.us/j/621951121 [cmu.zoom.us]
Meeting ID: 621 951 121
TITLE: Some progress on the unique ergodicity problem
ABSTRACT: In 2005, Kechris, Pestov and Todorcevic exhibited a
correspondence between combinatorial properties of structures and
dynamical properties of their automorphism groups. In 2012, Angel, Kechris
and Lyons used this correspondence to show the unique ergodicity of all
the actions of some subgroups of $S_\infty$. In this talk, I will give an
overview of the aforementioned results and discuss recent work
generalizing results of Angel, Kechris and Lyons.
TUESDAY, April 20, 2021
Mathematical logic seminar: 3:30 P.M., Online, Sandra Müller, University
of Vienna
Join Zoom Meeting: https://cmu.zoom.us/j/621951121 [cmu.zoom.us]
Meeting ID: 621 951 121
TITLE: TBA
TUESDAY, April 20, 2021
Set Theory Reading Group: 4:30 P.M., Online, Sandra Müller, University of
Vienna
Join Zoom Meeting: https://cmu.zoom.us/j/621951121 [cmu.zoom.us]
Meeting ID: 621 951 121
TITLE: TBA
TUESDAY, April 27, 2021
Mathematical logic seminar: 3:30 P.M., Online, Omer Ben-Neria, The Hebrew
University of Jerusalem
Join Zoom Meeting: https://cmu.zoom.us/j/621951121 [cmu.zoom.us]
Meeting ID: 621 951 121
TITLE: Tree-like scales and free subsets of set theoretic algebras, part 1
TUESDAY, April 27, 2021
Set Theory Reading Group: 4:30 P.M., Online, Omer Ben-Neria, The Hebrew
University of Jerusalem
Join Zoom Meeting: https://cmu.zoom.us/j/621951121 [cmu.zoom.us]
Meeting ID: 621 951 121
TITLE: Tree-like scales and free subsets of set theoretic algebras, part 2
Talk tomorrow by Alan Dow (1 30 pm)
Toronto Set Theory Seminar
3/4/2021 13:30:00
Hello everyone,
Please use the following link and fill the form (every week) to enter the meeting. This form helps the Field Institute to know statistical data about attendance.
Here the speaker information:
Date and Time: Friday, March 5th, 2021 - 1:30pm to 3:00pm
Title: On the cardinality of separable pseudoradial spacesAbstract:
A point is in the radial closure of a set A if there is a well-ordered sequence from A converging to the point. A set is radially closed if all points in the radial closure are in the set. A space is radial if the radial closure of a set equals its closure and is pseudoradial if every radially closed set is closed.
One can observe that the notions of Frechet-Urysohn and sequential are the related notions when restricted to the usual countable sequences. Motivatedby some work and questions by Santi Spadaro, Istvan Juhasz asked about the implicit question raised by the title. We discuss our progress on the problem in joint work with Istvan Juhasz.
Iván Ongay Valverde (he/his)
Alexandra Pasi: Forcing $\aleph_1$-Free Groups to Be Free
PALS
3/3/2021
Tuesday (March 9) at 1pm MST
Zoom Meeting ID:
https://cuboulder.zoom.us/j/96896272260
Passcode: PALS2021
Speaker: Alexandra Pasi (Baylor)
Title: Forcing $\aleph_1$-Free Groups to Be Free
Abstract: $\aleph_1$-free groups, abelian groups whose countable subgroups are free, are objects of both algebraic and set-theoretic interest. Illustrating this, we note that $\aleph_1$-free groups, and in particular the question of when $\aleph_1$-free groups are free, were central to the resolution of the Whitehead problem as undecidable. In elucidating the relationship between $\aleph_1$-freeness and freeness, we prove the following result: an abelian group $G$ is $\aleph_1$-free in a countable transitive model of $\operatorname{ZFC}$ (and thus by absoluteness, in every transitive model of $\operatorname{ZFC}$) if and only if it is free in some generic model extension. We would like to answer the more specific question of when an $\aleph_1$-free group can be forced to be free while preserving the cardinality of the group. For groups of size $\aleph_1$, we establish a necessary and sufficient condition for when such forcings are possible. We also identify a number of existing and novel forcings which force such $\aleph_1$-free groups of size $\aleph_1$ to become free with cardinal preservation. These forcings lay the groundwork for a larger project which uses forcing to explore various algebraic properties of $\aleph_1$-free groups and develops new set-theoretical tools for working with them.
Tagged: Alexandra Pasi
Fwd: Fw: Kobe Set Theory Workshop 2021 -- on the occasion of Sakaé Fuchino's retirement --
Toronto Set Theory Seminar
3/3/2021 9:00:00
An interesting workshop
Iván Ongay Valverde (he/his)
EXTERNAL EMAIL:
dear colleague,
we will have a zoom workshop at Kobe University on the occasion of
Sakaé Fuchino's retirement from March 9 (tue) till March 11 (thu).
(Sakaé retired last year and the originally planned workshop was
cancelled because of COVID. we now decided to have it online.)
see
for the program etc.
invited speakers are:
- Sakaé Fuchino
- David Asperó (University of East Anglia)
- Joan Bagaria (University of Barcelona)
- Piotr Borodulin-Nadzieja (University of Wrocław)
- Andrew Brooke-Taylor (University of Leeds)
- Joel David Hamkins (Oxford University)
- Daisuke Ikegami (Shibaura Institute of Technology)
- Chris Lambie-Hanson (Virginia Commonwealth University)
- Paul Larson (Miami University)
- Diego Mejía (Shizuoka University)
- Toshimichi Usuba (Waseda University)
- Teruyuki Yorioka (Shizuoka University)
anybody can attend, but a preregistration via zoom at the following page is
necessary:
once you register you should get a link for the zoom meeting within one day.
we'd be grateful if you could distribute this information to colleagues.
we very much hope that you can attend online.
best wishes,
jörg brendle
Talk this Friday by Alan Dow (1 30 pm)
Toronto Set Theory Seminar
3/2/2021 18:40:55
Hello everyone,
Please use the following link and fill the form (every week) to enter the meeting. This form helps the Field Institute to know statistical data about attendance.
Here the speaker information:
Date and Time: Friday, March 5th, 2021 - 1:30pm to 3:00pm
Title: On the cardinality of separable pseudoradial spacesAbstract:
A point is in the radial closure of a set A if there is a well-ordered sequence from A converging to the point. A set is radially closed if all points in the radial closure are in the set. A space is radial if the radial closure of a set equals its closure and is pseudoradial if every radially closed set is closed.
One can observe that the notions of Frechet-Urysohn and sequential are the related notions when restricted to the usual countable sequences. Motivatedby some work and questions by Santi Spadaro, Istvan Juhasz asked about the implicit question raised by the title. We discuss our progress on the problem in joint work with Istvan Juhasz.
Iván Ongay Valverde (he/his)
Kobe Set Theory Workshop 2021: March 9-11
Conference
3/1/2021
Hello everyone.
Last year, Sakaé Fuchino retired from Kobe University. On this occasion, we will have the following online workshop. We look forward to your participation!
Kobe Set Theory Workshop 2021
— on the occasion of Sakaé Fuchino’s retirement —
(Online Workshop via ZOOM)
Dates: March 9th (Tue.) — 11th (Thu.)
Webpage: http://www2.kobe-u.ac.jp/~hsakai/Fuchino2021/
Speakers:
- Sakaé Fuchino (Kobe University)
- Joan Bagaria (University of Barcelona)
- Joel David Hamkins (Oxford University)
- Paul Larson (Miami University)
- David Aspero (University of East Anglia)
- Piotr Borodulin-Nadzieja (University of Wrocław)
- Andrew Brooke-Taylor (University of Leeds)
- Chris Lambie-Hanson (Virginia Commonwealth University)
- Teruyuki Yorioka (Shizuoka University)
- Toshinmichi Usuba (Waseda University)
- Daisuke Ikegami (Shibaura Institute of Technology)
- Diego Mejia (Shizuoka University)
Registration: Only registered participants will have access to the ZOOM Meeting link. For the registration, please click the following link.
https://kobe-u-ac-jp.zoom.us/meeting/register/tZYqde2oqjstH9QW5CXr6eWuUM3oMdbQ7xFE
After the registration, organizers will approve it within a day. Then, you will receive the ZOOM Meeting link by e-mail.
If you have any questions, please contact Hiroshi Sakai by e-mail.
Contact: hsakai@people.kobe-u.ac.jp
Tagged: Sakaé Fuchino, Joan Bagaria, Joel David Hamkins, Paul Larson, David Aspero, Piotr Borodulin-Nadzieja, Andrew Brooke-Taylor, Chris Lambie-Hanson, Teruyuki Yorioka, Toshinmichi Usuba, Daisuke Ikegami, Diego Mejia
(KGRC) research seminar talk on Thursday, March 4
Kurt Godel Research Center
3/1/2021 12:24:31
Research seminar
Kurt Gödel Research Center
Thursday, March 4
"Asymptotic differential algebra and logarithmic transseries"
Allen Gehret (KGRC)
In this talk I will give a brief introduction to the subject 'Asymptotic
Differential Algebra' and an overview of the logarithmic transseries programme.
The intuition originates in freshman calculus (specifically: limits,
l'hopital's rule, convergence/divergence of integrals and series, asymptotic
expansions). The mathematical concepts primarily involve various flavors of
fields (equipped with a derivation and/or a valuation and/or an ordering). The
logical content will be minimal: first-order languages, model completeness,
quantifier elimination.
Time and Place
Talk at 3:00pm via Zoom: This talk will be given via Zoom. If you have not
received the meeting link by the day before the talk, please contact
richard.springer@univie.ac.at!
This Week in Logic at CUNY
This Week in Logic at CUNY
2/28/2021 22:00:41
This Week in Logic at CUNY:
- - - - Monday, Mar 1, 2021 - - - -
Logic and Metaphysics Workshop
Date: Monday, Mar 1, 4.15-6.15 (NY time)
Shay Logan (Kansas State)
Title: The Easy Argument Against Noncontractive Logics Doesn’t Work
Abstract: The Easy Argument against noncontractivism is the argument that essentially amounts to pointing out that contraction is just repeating oneself. The purpose of this talk is to explain why the Easy Argument fails. I show first that the Easy Argument fails by being insufficiently precise, since there are many ways we can combine premises in an argument. After correcting for this, the Easy Argument then fails by being straightforwardly invalid. The premises required to correct for *this* failure, however, have controversial consequences. Altogether, it seems arguments against noncontractive logics, if there are any, will be Hard—not Easy—Arguments.
- - - - Tuesday, Mar 2, 2021 - - - -
Models of Peano Arithmetic (MOPA)
Tuesday, Mar 2, 7pm
The seminar will take place virtually at 7pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. Ali Enayat, University of Gothenburg
PA with a class of indiscernibles
This talk focuses on the theory PAI (I for Indiscernibles), a theory formulated in the language of PA augmented with a unary predicate I(x). Models of PAI are of the form (M,I) where (1) M is a model of PA, (2) I is a proper class of M, i.e., I is unbounded in M and (M,I) satisfies PA*, and (3) I forms a class of indiscernibles over M. The formalizability of the Infinite Ramsey Theorem in PA makes it clear that PAI is a conservative extension of PA. As we will see, nonstandard models of PA (of any cardinality) that have an expansion to a model of PAI are precisely those nonstandard models PA that can carry an inductive partial satisfaction class. The formulation and investigation of PAI was inspired by my work on the set theoretical sibling ZFI of PAI, whose behavior I will also compare and contrast with that of PAI.
- - - - Wednesday, Mar 3, 2021 - - - -
The New York City Category Theory Seminar
Date and Time: Wednesday Mar 3, 2021, 7:00 - 8:30 PM., on Zoom.
Speaker: Joshua Sussan, Medgar Evers, CUNY.
Title: Categorification and quantum topology.
Abstract: The Jones polynomial of a link could be defined through the representation theory of quantum sl(2). It leads to a 3-manifold invariant and 2+1 dimensional TQFT. In the mid 1990s, Crane and Frenkel outlined the categorification program with the aim of constructing a 3+1 dimensional TQFT by upgrading the representation theory of quantum sl(2) to some categorical structures. We will review these ideas and give examples of various categorifications of quantum sl(2) constructions.
- - - - Thursday, Mar 4, 2021 - - - -
Philog seminar
Thursday March 4 at 6:30 PM
Jenn McDonald, CUNY Graduate Center
Causal Models as Relative to Modal Profile
Abstract A recent development in the philosophy of causation uses the framework of causal models, such as structural equation models, to define actual causation. There are two components to such a definition. The first is to identify how to define causation in terms of a given model or given class of models. The second is to provide an account of what qualifies models as given – or apt – such that they can be plugged into the first stage. A naïve hypothesis is that a model is apt just in case it is accurate. In this talk I will argue, however, that the accuracy of a model is not a determinate function of a model, an interpretation, and a situation. A given model on a given interpretation can still be deemed accurate or inaccurate of the same situation. As I demonstrate, this is because accuracy is relative to a set of background possibilities – what I call a modal profile. I argue that this reveals a heretofore hidden element in how causal models represent – that models represent situations only relative to some modal profile or other. I propose that this calls for an additional component of an interpretation: an interpretation is an assignment of content to the variables and a specification of modal profile.
A zoom link will be posted on https://philog.arthurpaulpedersen.org/
Next speaker: Nur Dean, Farmingdale College
- - - - Friday, Mar 5, 2021 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, Mar 5, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. Hiroshi Sakai, Kobe University
Generalized stationary reflection and cardinal arithmetic
The stationary reflection principle, which is often called the Weak Reflection Principle, is known to have many interesting consequences. As for cardinal arithmetic, it implies that λω=λλω=λ for all regular cardinal λ≥ω2λ≥ω2. In this talk, we will discuss higher analogues of this stationary reflection principle and their consequences on cardinal arithmetic.
Next Week in Logic at CUNY:
- - - - Monday, Mar 8, 2021 - - - -
Logic and Metaphysics Workshop
Date: Monday, Mar 8, 4.15-6.15 (NY time)
Hitoshi Omori (Bochum)
Title: Two applications of Herzberger’s semantics
Abstract: In his paper “Dimensions of truth”, Hans Herzberger develops a semantic framework that captures both classical logic and weak Kleene logic through one and the same interpretation. The aim of this talk is to apply the simple idea of Herzberger to two kinds of many-valued semantics. This application will be led by the following two questions.
(i) Is de Finetti conditional a conditional?
(ii) What do CL, K3 and LP disagree about?
Note: This is a joint work with Jonas R. B. Arenhart (Santa Catarina).
- - - - Tuesday, Mar 9, 2021 - - - -
Models of Peano Arithmetic (MOPA)
Tuesday, Mar 9, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. Damir Dzhafarov, University of Connecticut
- - - - Wednesday, Mar 10, 2021 - - - -
- - - - Thursday, Mar 11, 2021 - - - -
- - - - Friday, Mar 12, 2021 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, Mar 12, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. Hossein Lamei Ramandi, Cornell University
Galvin's question on non-σσ-well ordered linear orders
Assume CC is the class of all linear orders LL such that LL is not a countable union of well ordered sets, and every uncountable subset of LL contains a copy of ω1ω1. We show it is consistent that CC has minimal elements. This answers an old question due to Galvin.
- - - - Other Logic News - - - -- - - - Web Site - - - -"Find us on the web at: nylogic.github.io(site designed, built & maintained by Victoria Gitman)"-------- ADMINISTRIVIA --------To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.
Talk by Justin Moore tomorrow (1 30pm)
Toronto Set Theory Seminar
2/25/2021 13:30:00
Hello everyone,
Please use the following link and fill the form (every week) to
enter the meeting. This form helps the Field Institute to know
statistical data about attendance.
Here the speaker information:
Date and Time: Friday, February 26, 2021 - 1:30pm to 3:00pm
Title: On the additivity of strong homology for locally compact separable metric spaces
Abstract:
We show that it is consistent relative to a weakly compact cardinal that
strong homology is additive and compactly supported within the class of
locally compact separable metric spaces. This complements work of
Mardešić and Prasolov showing that the Continuum Hypothesis implies that
a countable sum of Hawaiian earrings witnesses the failure of strong
homology to possess either of these properties. Our results build
directly on work of Lambie-Hanson and the second author which
establishes the consistency, relative to a weakly compact cardinal, of
$\lim^{s}A=0$ for all $s\geq 1$ for a certain pro-abelian group $A$; we show that that work's arguments carry implications for the vanishing and additivity of the $\lim^{s}$ functors over a substantially more general class of pro-abelian groups indexed by $\mathbb{N}^{\mathbb{N}}$.
This is joint work with Nathaniel Bannister and Jeffrey Bergfalk.
Iván Ongay Valverde (he/his)
Logic Seminar Wed 3 March 2021 17:00 hrs at NUS
NUS Logic Seminar
2/24/2021 5:24:44
Invitation to the Logic Seminar at the National University of Singapore
Date: Wednesday, 3 March 2021, 17:00 hrs
Talk via Zoom: https://nus-sg.zoom.us/j/96860201432?pwd=cVdwZmd2clVFaEhaTmJjaGdXMFdmdz09
Meeting ID: 968 6020 1432
Password: Is P=NP?
Speaker: Desmond Lau
Title: On the unification of two "maximal" axioms
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Abstract: Martin's Maximum^{++} and Woodin's axiom (*) are two
statements independent of, but consistent with, ZFC. I will present
the common reasons they are appealing as set-theoretic axioms, before
comparing the sense in which they are "maximal". I will also run
through an exposition of the recent work by Aspero and
Schindler, which shows Martin's Maximum^{++} implies (*), effectively
"unifying" the statements.
Talk by Justin Moore this Friday (1 30 pm)
Toronto Set Theory Seminar
2/23/2021 9:00:26
Hello everyone,
I sent an email instead of scheduling it, so I send the correct subject again to avoid confusion. Justin's talk will be this Friday.
Please use the following link and fill the form (every week) to
enter the meeting. This form helps the Field Institute to know
statistical data about attendance.
Here the speaker information:
Date and Time: Friday, February 26, 2021 - 1:30pm to 3:00pm
Title: On the additivity of strong homology for locally compact separable metric spaces
Abstract:
We show that it is consistent relative to a weakly compact cardinal that
strong homology is additive and compactly supported within the class of
locally compact separable metric spaces. This complements work of
Mardešić and Prasolov showing that the Continuum Hypothesis implies that
a countable sum of Hawaiian earrings witnesses the failure of strong
homology to possess either of these properties. Our results build
directly on work of Lambie-Hanson and the second author which
establishes the consistency, relative to a weakly compact cardinal, of
$\lim^{s}A=0$ for all $s\geq 1$ for a certain pro-abelian group $A$; we show that that work's arguments carry implications for the vanishing and additivity of the $\lim^{s}$ functors over a substantially more general class of pro-abelian groups indexed by $\mathbb{N}^{\mathbb{N}}$.
This is joint work with Nathaniel Bannister and Jeffrey Bergfalk.
Iván Ongay Valverde (he/his)
Talk by Justin Moore this Friday (1 30 pm)
Toronto Set Theory Seminar
2/23/2021 8:46:15
Hello everyone,
Please use the following link and fill the form (every week) to
enter the meeting. This form helps the Field Institute to know
statistical data about attendance.
Here the speaker information:
Date and Time: Friday, February 26, 2021 - 1:30pm to 3:00pm
Title: On the additivity of strong homology for locally compact separable metric spaces
Abstract:
We show that it is consistent relative to a weakly compact cardinal that
strong homology is additive and compactly supported within the class of
locally compact separable metric spaces. This complements work of
Mardešić and Prasolov showing that the Continuum Hypothesis implies that
a countable sum of Hawaiian earrings witnesses the failure of strong
homology to possess either of these properties. Our results build
directly on work of Lambie-Hanson and the second author which
establishes the consistency, relative to a weakly compact cardinal, of
$\lim^{s}A=0$ for all $s\geq 1$ for a certain pro-abelian group $A$; we show that that work's arguments carry implications for the vanishing and additivity of the $\lim^{s}$ functors over a substantially more general class of pro-abelian groups indexed by $\mathbb{N}^{\mathbb{N}}$.
This is joint work with Nathaniel Bannister and Jeffrey Bergfalk.
Iván Ongay Valverde (he/his)
Talk by Justin Moore tomorrow (1 30pm)
Toronto Set Theory Seminar
2/23/2021 8:50:04
Hello everyone,
Please use the following link and fill the form (every week) to
enter the meeting. This form helps the Field Institute to know
statistical data about attendance.
Here the speaker information:
Date and Time: Friday, February 26, 2021 - 1:30pm to 3:00pm
Title: On the additivity of strong homology for locally compact separable metric spaces
Abstract:
We show that it is consistent relative to a weakly compact cardinal that
strong homology is additive and compactly supported within the class of
locally compact separable metric spaces. This complements work of
Mardešić and Prasolov showing that the Continuum Hypothesis implies that
a countable sum of Hawaiian earrings witnesses the failure of strong
homology to possess either of these properties. Our results build
directly on work of Lambie-Hanson and the second author which
establishes the consistency, relative to a weakly compact cardinal, of
$\lim^{s}A=0$ for all $s\geq 1$ for a certain pro-abelian group $A$; we show that that work's arguments carry implications for the vanishing and additivity of the $\lim^{s}$ functors over a substantially more general class of pro-abelian groups indexed by $\mathbb{N}^{\mathbb{N}}$.
This is joint work with Nathaniel Bannister and Jeffrey Bergfalk.
Iván Ongay Valverde (he/his)
Barcelona Set theory Seminar
Barcelona Logic Seminar
2/22/2021 3:54:44
Dear All,
Please find attached the announcement of the next session of the Barcelona Set Theory Seminar. Feel free to distribute it.
SPEAKER: Brent Cody (Virginia Commonwealth University)
TITLE: Higher indescribability and ideal operators
DATE: 24 February 2021
TIME: 16:00 (CET)
PLACE: The Seminar will take place online at the following address:
Best regards,
Joan
P.S.: If you do not wish to receive any more announcements, please send an email to
bagaria@ub.edu with the text “Unsubscribe”.
Joan Bagaria
ICREA Research Professor
Universitat de Barcelona
Departament de Matemàtiques i Informàtica
Gran Via de les Corts Catalanes 585
08007 Barcelona
Catalonia
Phone: +34 93 402 1609
Barcelona Set theory Seminar
Barcelona Logic Seminar
2/22/2021 3:14:04
Dear All,
Please find attached the announcement of the next session of the Barcelona Set Theory Seminar. Feel free to distribute it.
SPEAKER: Brent Cody (Virginia Commonwealth University)
TITLE: Higher indescribability and ideal operators
DATE: 24 February 2021
TIME: 16:00 (CET)
PLACE: The Seminar will take place online at the following address:
Best regards,
Joan
P.S.: If you do not wish to receive any more announcements, please send an email to
bagaria@ub.edu with the text “Unsubscribe”.
Joan Bagaria
ICREA Research Professor
Universitat de Barcelona
Departament de Matemàtiques i Informàtica
Gran Via de les Corts Catalanes 585
08007 Barcelona
Catalonia
Phone: +34 93 402 1609
This Week in Logic at CUNY
This Week in Logic at CUNY
2/21/2021 20:49:41
This Week in Logic at CUNY:
- - - - Monday, Feb 22, 2021 - - - -
Logic and Metaphysics Workshop
Date: Monday, Feb 22, 4.15-6.15 (NY time)
Speaker: Graham Priest (CUNY)
Title: Substructural Solutions to the Semantic Paradoxes: a Dialetheic Perspective
Abstract: Over the last decade or so, a number of writers have argued for solutions to the paradoxes of semantic self-reference which proceed by dropping some of the structural rules of inference, most notably Cut and/or Contraction. In this paper, we will examine such accounts, with a particular eye on their relationship to more familiar dialetheic accounts.
- - - - Tuesday, Feb 23, 2021 - - - -Models of Peano Arithmetic (MOPA)
Tuesday, Feb 23, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. Corey Switzer, University of ViennaIndependence in PA: The Method of (L,n)(L,n)-Models
The purpose of this talk is to exposit a method for proving independence over PA of 'mathematical' statements (whatever that means). The method uses the concept of an (L,n)(L,n)-model: a finite sequence of finite LL-structures for some first order LL extending the language of arithmetic. The idea is that this finite sequence is intended to represent increasing approximations of a potentially infinite structure and the machinery developed allows one to translate (meta-mathematical) compactness type statements, which are easily seen to be independent of PA, into statements about finite combinatorics, which have 'mathematical content'. (L,n)(L,n)-models were introduced by Shelah in the 70's in his alternative proof of the Paris-Harrington Theorem and also appears (implicitly) in his example of a true, unprovable Π01Π10 statement of some 'mathematical' content. A similar idea was discovered independently by Kripke (unpublished). In this talk we will flesh out the details of this method and extend the general theory. This will allow us to present, in a fairly systematic fashion, proofs of the Paris-Harrington Theorem and the independence over PA of several, similar, Ramsey Theoretic statements including some which are Π01Π10.
- - - - Wednesday, Feb 24, 2021 - - - -
- - - - Thursday, Feb 25, 2021 - - - -
Philog Seminar
Thursday, Feb 25, 6:30 PM
Rohit Parikh
Covid-19 and knowledge based computation
Abstract: the purpose of this project is to combine insights from the logic of knowledge (act according to what you know), and graph theory (spread of infection follows the edges of a graph). We show how knowledge based algorithms can be used to combine safety with economic and social activity.
A Zoom link will be posted on
https://philog.arthurpaulpedersen.org/ - - - - Friday, Feb 26, 2021 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, Feb 26, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. Farmer Schlutzenberg, University of Münster
(Non)uniqueness and (un)definability of embeddings beyond choice
Work in ZF and let j:Vα→Vαj:Vα→Vα be an elementary, or partially elementary, embedding. One can examine the degree of uniqueness, definability or constructibility of jj. For example, is there β<αβ<α such that jj is the unique (partially) elementary extension of j↾Vβj↾Vβ? Is jj definable from parameters over VαVα? We will discuss some results along these lines, illustrating that answers can depend heavily on circumstances. Some of the work is due independently and earlier to Gabriel Goldberg.
Next Week in Logic at CUNY:
- - - - Monday, Mar 1, 2021 - - - -
Logic and Metaphysics Workshop
Date: Monday, Mar 1, 4.15-6.15 (NY time)
Shay Logan (Kansas State)
Title: The Easy Argument Against Noncontractive Logics Doesn’t Work
Abstract: The Easy Argument against noncontractivism is the argument that essentially amounts to pointing out that contraction is just repeating oneself. The purpose of this talk is to explain why the Easy Argument fails. I show first that the Easy Argument fails by being insufficiently precise, since there are many ways we can combine premises in an argument. After correcting for this, the Easy Argument then fails by being straightforwardly invalid. The premises required to correct for *this* failure, however, have controversial consequences. Altogether, it seems arguments against noncontractive logics, if there are any, will be Hard—not Easy—Arguments.
- - - - Tuesday, Mar 2, 2021 - - - -
Models of Peano Arithmetic (MOPA)
Tuesday, Mar 2, 7pm
The seminar will take place virtually at 7pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. Ali Enayat, University of Gothenburg
PA with a class of indiscernibles
This talk focuses on the theory PAI (I for Indiscernibles), a theory formulated in the language of PA augmented with a unary predicate I(x). Models of PAI are of the form (M,I) where (1) M is a model of PA, (2) I is a proper class of M, i.e., I is unbounded in M and (M,I) satisfies PA*, and (3) I forms a class of indiscernibles over M. The formalizability of the Infinite Ramsey Theorem in PA makes it clear that PAI is a conservative extension of PA. As we will see, nonstandard models of PA (of any cardinality) that have an expansion to a model of PAI are precisely those nonstandard models PA that can carry an inductive partial satisfaction class. The formulation and investigation of PAI was inspired by my work on the set theoretical sibling ZFI of PAI, whose behavior I will also compare and contrast with that of PAI.
- - - - Wednesday, Mar 3, 2021 - - - -
The New York City Category Theory Seminar
Date and Time: Wednesday Mar 3, 2021, 7:00 - 8:30 PM., on Zoom.
Speaker: Joshua Sussan, Medgar Evers, CUNY.
Title: Categorification and quantum topology.
Abstract: The Jones polynomial of a link could be defined through the representation theory of quantum sl(2). It leads to a 3-manifold invariant and 2+1 dimensional TQFT. In the mid 1990s, Crane and Frenkel outlined the categorification program with the aim of constructing a 3+1 dimensional TQFT by upgrading the representation theory of quantum sl(2) to some categorical structures. We will review these ideas and give examples of various categorifications of quantum sl(2) constructions.
- - - - Thursday, Mar 4, 2021 - - - -
- - - - Friday, Mar 5, 2021 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, Mar 5, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. Hiroshi Sakai, Kobe University
Generalized stationary reflection and cardinal arithmetic
The stationary reflection principle, which is often called the Weak Reflection Principle, is known to have many interesting consequences. As for cardinal arithmetic, it implies that λω=λλω=λ for all regular cardinal λ≥ω2λ≥ω2. In this talk, we will discuss higher analogues of this stationary reflection principle and their consequences on cardinal arithmetic.
- - - - Other Logic News - - - -- - - - Web Site - - - -"Find us on the web at: nylogic.github.io(site designed, built & maintained by Victoria Gitman)"-------- ADMINISTRIVIA --------To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.
Talk by Assaf Rinot tomorrow (1 30 pm)
Toronto Set Theory Seminar
2/18/2021 13:30:00
Hello everyone,
Please use the following link and fill the form (every week) to
enter the meeting. This form helps the Field Institute to know
statistical data about attendance.
Here the speaker information:
Date and Time: Friday, February 19, 2021 - 1:30pm to 3:00pm
Title:
All colorings are strong - but some colorings are stronger than
the others.
Abstract: Strong colorings are everywhere - they can be obtained from
analysis of basis problems, transfinite diagonalizations, oscillations,
or walks on ordinals. They give rise to interesting topological spaces
and partial orders.
In this talk, I'll be looking at all aspects mentioned above, reporting
on findings from my joint projects with Kojman, Lambie-Hanson, Inamdar,
Steprans and Zhang.
Iván Ongay Valverde (he/his)
Barcelona Set theory Seminar
Barcelona Logic Seminar
2/15/2021 5:42:45
Dear All,
Please find attached the announcement of the next session of the Barcelona Set Theory Seminar. Feel free to distribute it.
SPEAKER: Hiroshi Sakai (Kobe University)
TITLE: Generalized Stationary Reflection and Cardinal Arithmetic
TIME: 16:00 (CET)
PLACE: The Seminar will take place online at the following address:
Best regards,
Joan
P.S.: If you do not wish to receive any more announcements, please send an email to
bagaria@ub.edu with the text “Unsubscribe”.
Joan Bagaria
ICREA Research Professor
Universitat de Barcelona
Departament de Matemàtiques i Informàtica
Gran Via de les Corts Catalanes 585
08007 Barcelona
Catalonia
Phone: +34 93 402 1609
Talk by Assaf Rinot Friday (1 30pm)
Toronto Set Theory Seminar
2/15/2021 0:44:03
Hello everyone,
Please use the following link and fill the form (every week) to
enter the meeting. This form helps the Field Institute to know
statistical data about attendance.
Here the speaker information:
Date and Time: Friday, February 19, 2021 - 1:30pm to 3:00pm
Title:
All colorings are strong - but some colorings are stronger than
the others.
Abstract: Strong colorings are everywhere - they can be obtained from
analysis of basis problems, transfinite diagonalizations, oscillations,
or walks on ordinals. They give rise to interesting topological spaces
and partial orders.
In this talk, I'll be looking at all aspects mentioned above, reporting
on findings from my joint projects with Kojman, Lambie-Hanson, Inamdar,
Steprans and Zhang.
Iván Ongay Valverde (he/his)
This Week in Logic at CUNY
This Week in Logic at CUNY
2/14/2021 20:59:41
This Week in Logic at CUNY:
- - - - Monday, Feb 15, 2021 - - - -
- - - - Tuesday, Feb 16, 2021 - - - -
Models of Peano Arithmetic (MOPA)
Tuesday, Feb 16, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. Mateusz Łełyk, University of Warsaw
Nonequivalent axiomatizations of PAPA and the Tarski Boundary
We study a family of axioms expressing‘All axioms of PA are true.' (*)‘All axioms of PA are true.' (*)where PA denotes Peano Arithmetic. More precisely, each such axiom states that all axioms from a chosen axiomatization of PA are true. We start with a very natural theory of truth CT−(PA)CT−(PA) which is a finite extension of PA in the language of arithmetic augmented with a fresh predicate T to serve as a truth predicate for the language of arithmetic. Additional axioms of this theory are straightforward translations of inductive Tarski truth conditions. To study various possible ways of expressing (*), we investigate extensions of CT−(PA)CT−(PA) with axioms of the form∀x(δ(x)→T(x)).∀x(δ(x)→T(x)).In the above (and throughout the whole abstract) δ(x)δ(x) is an elementary formula which is proof-theoretically equivalent to the standard axiomatization of PA with the induction scheme, i.e. the equivalence∀x(Provδ(x)≡ProvPA(x)).∀x(Provδ(x)≡ProvPA(x)).is provable in IΣ1IΣ1. For every such δδ, the extension of CT−(PA)CT−(PA) with the above axiom will be denoted CT−[δ]CT−[δ].
In particular we shall focus on the arithmetical strength of theories CT−[δ]CT−[δ]. The 'line' demarcating extensions of CT−(PA)CT−(PA) which are conservative over PA from the nonconservative ones is known in the literature as the Tarski Boundary. For some time, there seemed to be the least (in terms of deductive strength) *natural* extension of CT−(PA)CT−(PA) on the nonconservative side of the boundary, whose one axiomatization is given by CT−(PA)CT−(PA) and Δ0Δ0 induction for the extended language (the theory is called CT0CT0). This theory can equivalently be axiomatized by adding to CT−(PA)CT−(PA) the natural formal representation of the statement 'All theorems of PAPA are true.'. We show that the situation between the Tarski Boundary and CT0CT0 is much more interesting:
Theorem 1: For every r.e. theory Th in the language of arithmetic the following are equivalent:
1) CT0⊢CT0⊢ Th
2) there exists δδ such that CT−[δ]CT−[δ] and Th have the same arithmetical consequences.
Theorem 1 can be seen as a representation theorem for r.e. theories below REFω(PA)REFω(PA) (all finite iterations of uniform reflection over PAPA, which is the set of arithmetical consequences of CT0CT0): each such theory can be finitely axiomatized by a theory of the form CT−[δ]CT−[δ], where δδ is proof-theoretically reducible to PAPA.
Secondly, we use theories CT−[δ]CT−[δ] to investigate the situation below the Tarski Boundary. We shall prove the following result
Theorem 2: There exists a family {δf}f∈ω<ω{δf}f∈ω<ω such that for all f,g∈ω<ωf,g∈ω<ω
1) CT−[δf]CT−[δf] is conservative over PAPA;
2) if f⊊gf⊊g, then CT−[δg]CT−[δg] properly extends CT−[δf]CT−[δf];
3) if f⊥gf⊥g then CT−[δg]∪CT−[δf]CT−[δg]∪CT−[δf] is nonconservative over PAPA (but consistent).
- - - - Wednesday, Feb 17, 2021 - - - -
The New York City Category Theory Seminar
Speaker: Richard Blute, University of Ottawa.
Date and Time: Wednesday February 17, 2021, 7:00 - 8:30 PM., on Zoom.
Title: Finiteness Spaces, Generalized Polynomial Rings and Topological Groupoids.
Abstract: The category of finiteness spaces was introduced by Thomas Ehrhard as a model of classical linear logic, where a set is equipped with a class of subsets to be thought of as finitary. Morphisms are relations preserving the finitary structure. The notion of finitary subset allows for a sharp analysis of computational structure.
Working with finiteness spaces forces the number of summands in certain calculations to be finite and thus avoid convergence questions. An excellent example of this is how Ribenboim’s theory of generalized power series rings can be naturally interpreted by assigning finiteness monoid structure to his partially ordered monoids. After Ehrhard’s linearization construction is applied, the resulting structures are the rings of Ribenboim’s construction.
There are several possible choices of morphism between finiteness spaces. If one takes structure-preserving partial functions, the resulting category is complete, cocomplete and symmetric monoidal closed. Using partial functions, we are able to model topological groupoids, when we consider composition as a partial function. We can associate to any hemicompact etale Hausdorff groupoid a complete convolution ring. This is in particular the case for the infinite paths groupoid associated to any countable row-finite directed graph.
- - - - Thursday, Feb 18, 2021 - - - -
- - - - Friday, Feb 19, 2021 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, Feb 19, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. Philipp Lücke, University of Bonn
Magidor-style embedding characterizations of large cardinals
Motivated by a classical theorem of Magidor, I will present results providing characterizations of important objects from the lower end of the large cardinal hierarchy through the existence of elementary embeddings between set-sized models that map their critical point to the large cardinal in question. Focusing on the characterization of shrewd cardinals, introduced by Rathjen in a proof-theoretic context, I will show how these results can be used in the study of the combinatorics of strong chain conditions and the investigation of principles of structural reflection formulated by Bagaria.
Next Week in Logic at CUNY:
- - - - Monday, Feb 22, 2021 - - - -
- - - - Tuesday, Feb 23, 2021 - - - -
Models of Peano Arithmetic (MOPA)
Tuesday, Feb 23, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. Corey Switzer, University of Vienna
- - - - Wednesday, Feb 24, 2021 - - - -
- - - - Thursday, Feb 25, 2021 - - - -
- - - - Friday, Feb 26, 2021 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, Feb 26, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. Farmer Schlutzenberg, University of Münster
(Non)uniqueness and (un)definability of embeddings beyond choice
Work in ZF and let j:Vα→Vαj:Vα→Vα be an elementary, or partially elementary, embedding. One can examine the degree of uniqueness, definability or constructibility of jj. For example, is there β<αβ<α such that jj is the unique (partially) elementary extension of j↾Vβj↾Vβ? Is jj definable from parameters over VαVα? We will discuss some results along these lines, illustrating that answers can depend heavily on circumstances. Some of the work is due independently and earlier to Gabriel Goldberg.
- - - - Other Logic News - - - -
- - - - Web Site - - - -
"Find us on the web at:
nylogic.github.io(site designed, built & maintained by Victoria Gitman)"
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Logic Seminar 17 Feb 2021 17:00 hrs at NUS by Xiao Ming
NUS Logic Seminar
2/14/2021 19:03:27
Invitation to the Logic Seminar at the National University of Singapore
Date: Wednesday, 17 February 2020, 17:00 hrs
Talk via Zoom: https://nus-sg.zoom.us/j/96860201432?pwd=cVdwZmd2clVFaEhaTmJjaGdXMFdmdz09
Meeting ID: 968 6020 1432
Password: Is P=NP?
Speaker: Xiao Ming
Title: Borel Order Dimensions
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Abstract: Order dimension is a classical combinatorial object and has been
widely studied by set theorists, combinatorists and computer scientists
since its introduction by Dushnik and Miller in 1941. We focus on the
partial orderings that are definable as a Borel subsets in a Polish space
and analyze the order dimension that can be realized by Borel definable
orders and show that there are some interesting behaviors that can be
quite different from the classical order dimension using arbitrary
realization. This is a joint work with Dilip Raghavan.
Upcoming CMU math logic events
Carnegie Mellon Logic Seminar
2/12/2021 19:46:37
TUESDAY, February 16, 2021
Mathematical logic seminar: 3:30 P.M., Online, Aristotelis
Panagiotopoulos, University of Muenster
Join Zoom Meeting: https://cmu.zoom.us/j/621951121 [cmu.zoom.us]
Meeting ID: 621 951 121
TITLE: The definable content of (co)homological invariants: Cech
cohomology
ABSTRACT: In this talk we will develop a framework for enriching various
classical invariants of homological algebra and algebraic topology with
additional descriptive set-theoretic information. The resulting "definable
invariants" can be used for much finer classification than their purely
algebraic counterparts. We will then illustrate how these ideas apply to
the classical Cech cohomology theory, by introducing a new invariant for
locally compact metrizable spaces up to homotopy equivalence which we call
"definable cohomology". In strong contrast to its classical counterpart,
this definable cohomology theory provides complete classification to
homotopy classes of mapping telescopes of d-tori, and for homotopy classes
of maps from mapping telescopes of d-tori to spheres. The latter problem
was raised in the d=1 case by Borsuk and Eilenberg in 1936.
This is joint work with Jeffrey Bergfalk and Martino Lupini.
TUESDAY, February 16, 2021
Set Theory Reading Group: 4:30 P.M., Online, Aristotelis Panagiotopoulos,
University of Muenster
Join Zoom Meeting: https://cmu.zoom.us/j/621951121 [cmu.zoom.us]
Meeting ID: 621 951 121
TITLE: Ulam stability for quotients of abelian non-archimedean Polish
groups
ABSTRACT: Based on an earlier work of Shelah concerning the relationship
of the continuum hypothesis to the cardinality of the set of automorphisms
of $\mathcal{P}(\omega)/\mathrm{fin}$, Velickovic showed that if such an
automorphism admits a Borel lift $\mathcal{P}(\omega)\to
\mathcal{P}(\omega)$, then it is of a certain "trivial" form. Similarly,
Kanovei and Reeken showed that if $N,M$ are countable dense subgroups of
$\mathbb{R}$, then every homomorphism $\mathbb{R}/N\to \mathbb{R}/M$ with
a Borel lift $\mathbb{R}\to \mathbb{R}$, is of a certain "trivial" form.
Kanovei and Reeken asked whether quotients of the $p$-adic groups satisfy
similar "Ulam stability" phenomena. In this talk, we will settle this
question by providing Ulam-stability phenomena for definable homomorphisms
$G/N\to H/M$ when $G,H$ are arbitrary abelian non-archimedean Polish
groups and $N,M$ are Polishable subgroups. We will then illustrate how
such rigidity results are in the heart of the definable cohomology theory
which we developed in the previous talk.
This is joint work with Jeffrey Bergfalk and Martino Lupini.
THURSDAY, February 18, 2021
Model Theory Seminar: 10:00 A.M., Online, Michael Lieberman, Brno
University of Technology
Join Zoom Meeting:
https://cmu.zoom.us/j/96301869290?pwd=Qk1zS0h6ZThmUnRpbmNLNkVJSjkrQT09
Meeting ID: 963 0186 9290
Passcode: 567655
TITLE: Induced and higher-dimensional stable independence, Part I
ABSTRACT: We introduce the notion of a stable independence relation on an
abstract category, generalizing the notions familiar from classical and
abstract model theory. We discuss certain useful properties of such
relations---chiefly, canonicity---and indicate that, in mu-AECs, the
existence of a stable independence notion has the expected relationship
with the failure of the order property.
We highlight an important special case, in which the category is derived
by restricting to a nice family of morphisms in a larger, locally
presentable category (e.g. R-modules with pure homomorphisms). Here we
find a surprisingly deep connection between the existence of a stable
independence notion and the structure of the family of morphisms. Joint
work with J. Rosický and S. Vasey.
THURSDAY, February 25, 2021
Model Theory Seminar: 10:00 A.M., Online, Michael Lieberman, Brno
University of Technology
Join Zoom Meeting:
https://cmu.zoom.us/j/96301869290?pwd=Qk1zS0h6ZThmUnRpbmNLNkVJSjkrQT09
Meeting ID: 963 0186 9290
Passcode: 567655
TITLE: Induced and higher-dimensional stable independence, Part II
ABSTRACT: We discuss the conditions under which a stable independence
relation can be pushed upward---induced---from a subcategory to the
category as a whole: namely, that the larger category is weakly stable and
the subcategory is sufficiently nicely embedded. While a model-theoretic
argument can be given, we suggest that the category-theoretic analog is
cleaner and more efficient.
This has immediate applications: the algebraic classes considered in
recent work of Mazari-Armida (torsion R-modules with pure monomorphisms,
torsion-free Abelian groups with pure embeddings, etc.) all have
weakly-stable independence notions. Thanks to Mazari-Armida's results on
Galois stability of such classes (and a few additional properties), it is
clear that in each case the subcategory of sufficiently saturated objects
has a stable independence notion: we conclude that the same holds of the
categories themselves.
Time permitting, we will also discuss the phenomenon of excellence---that
is, the existence of stable independence in all dimensions---in this
context. As it happens, in any category of the special form considered in
Part I (obtained by restricting to a nice class of morphisms in a nice
category), excellence follows directly from the existence of a stable
independence notion. Joint work with J. Rosický and S. Vasey.
TUESDAY, March 2, 2021
Mathematical logic seminar: 3:30 P.M., Online, Marc Noy, Technical
University of Catalonia
Join Zoom Meeting: https://cmu.zoom.us/j/621951121 [cmu.zoom.us]
Meeting ID: 621 951 121
TITLE: Zero-One and Convergence Laws for Graphs Embeddable on a Fixed
Surface
ABSTRACT: Let G be a class of labeled graphs with the uniform probability
distribution on graphs with a fixed number of vertices. Given a graph
property A, we are interested in the limiting probability that A holds in
G. It was shown by Heinig et al. that this limiting probability always
exists when G is the class of planar graphs and A is any property
expressible in monadic second order logic (MSO), and it was conjectured
that the same result holds for the class of graphs embeddable on a fixed
surface S. After reviewing the results for planar graphs, and more
generally for minor-closed classes of graphs, we will refute the
conjecture by showing that for every closed surface (orientable or not)
other than the sphere there exists an MSO graph property whose limiting
probability does not exist. In addition we show that every rational number
in [0,1] is the limiting probability of some MSO property, as opposed to
the class of planar graphs where there are so-called gaps. The proof
relies on a combination of methods from structural graph theory,
concretely large face-width embeddings of graphs on surfaces, analytic
combinatorics, and finite model theory.
This is joint work with Albert Atserias and Stephan Kreutzer.
TUESDAY, April 20, 2021
Mathematical logic seminar: 3:30 P.M., Online, Sandra Müller, University
of Vienna
Join Zoom Meeting: https://cmu.zoom.us/j/621951121 [cmu.zoom.us]
Meeting ID: 621 951 121
TITLE: TBA
TUESDAY, April 20, 2021
Set Theory Reading Group: 4:30 P.M., Online, Sandra Müller, University of
Vienna
Join Zoom Meeting: https://cmu.zoom.us/j/621951121 [cmu.zoom.us]
Meeting ID: 621 951 121
TITLE: TBA
Upcoming math logic events at CMU
Carnegie Mellon Logic Seminar
2/7/2021 20:37:38
TUESDAY, February 9, 2021
Mathematical logic seminar: 3:30 P.M., Online, Benjamin Siskind,
University of California, Berkeley
Join Zoom Meeting: https://cmu.zoom.us/j/621951121 [cmu.zoom.us]
Meeting ID: 621 951 121
TITLE: Order-preserving Martin’s Conjecture
ABSTRACT: Martin’s Conjecture is a precise way of asserting that, up to
equivalence, the only natural functions on the Turing degrees are the
familiar ones: the constant functions, the identity, the Turing jump, and
the transfinite iterates of the Turing jump. This conjecture is open even
restricted to low-level Borel functions, but there have been partial
results over the years which show it holds for classes of functions
meeting requirements orthogonal to definability. Our recent result is that
part of Martin’s Conjecture (lately called “part one”) holds for the class
of order-preserving functions. In particular, it follows that the full
Martin’s Conjecture holds for Borel order-preserving functions. We’ll talk
about Martin’s Conjecture broadly and say something about this recent
work. This is joint work with Patrick Lutz.
TUESDAY, February 9, 2021
Set Theory Reading Group: 4:30 P.M., Online, Benjamin Siskind, University
of California, Berkeley
Join Zoom Meeting: https://cmu.zoom.us/j/621951121 [cmu.zoom.us]
Meeting ID: 621 951 121
TITLE: Measure-preserving functions on the Turing degrees
ABSTRACT: One proof of part one of Martin’s Conjecture for
order-preserving functions works for a bigger class of functions: those
which are measure-preserving for the Martin measure, in the sense of
ergodic theory. Looking at this class of functions brings out more
set-theoretic aspects of Martin’s Conjecture. For example, part one of
Martin’s Conjecture is equivalent to the non-existence of other
non-principal ultrafilters on the Turing degrees Rudin-Keisler below the
Martin measure. We’ll talk about the proof of part one of Martin’s
Conjecture for this class of functions and some consequences. This is
joint work with Patrick Lutz.
THURSDAY, February 11, 2021
Model Theory Seminar: 10:00 A.M., Online, John Baldwin, UIC
Join Zoom Meeting:
https://cmu.zoom.us/j/96301869290?pwd=Qk1zS0h6ZThmUnRpbmNLNkVJSjkrQT09
Meeting ID: 963 0186 9290
Passcode: 567655
TITLE: The Hanf number for extendability is the first measurable cardinal,
Part 2
ABSTRACT: We prove in ZFC the existence of a complete sentence of
infinitary logic that has maximal models in a set of cardinals cofinal in
the first measurable but no maximal models in any cardinal beyond the
first measurable. As a warmup to the first lecture please look at the
Motivation http://homepages.math.uic.edu/~jbaldwin/pub/cmupre
This is joint work with Saharon Shelah.
Preprints are available at
http://homepages.math.uic.edu/~jbaldwin/pub/ahanfmaxjan21.pdf and
http://homepages.math.uic.edu/~jbaldwin/pub/ahazfjan7.pdf
TUESDAY, February 16, 2021
Mathematical logic seminar: 3:30 P.M., Online, Aristotelis
Panagiotopoulos, University of Muenster
Join Zoom Meeting: https://cmu.zoom.us/j/621951121 [cmu.zoom.us]
Meeting ID: 621 951 121
TITLE: The definable content of (co)homological invariants: Cech
cohomology
ABSTRACT: In this talk we will develop a framework for enriching various
classical invariants of homological algebra and algebraic topology with
additional descriptive set-theoretic information. The resulting "definable
invariants" can be used for much finer classification than their purely
algebraic counterparts. We will then illustrate how these ideas apply to
the classical Cech cohomology theory, by introducing a new invariant for
locally compact metrizable spaces up to homotopy equivalence which we call
"definable cohomology". In strong contrast to its classical counterpart,
this definable cohomology theory provides complete classification to
homotopy classes of mapping telescopes of d-tori, and for homotopy classes
of maps from mapping telescopes of d-tori to spheres. The latter problem
was raised in the d=1 case by Borsuk and Eilenberg in 1936.
This is joint work with Jeffrey Bergfalk and Martino Lupini.
TUESDAY, February 16, 2021
Set Theory Reading Group: 4:30 P.M., Online, Aristotelis Panagiotopoulos,
University of Muenster
Join Zoom Meeting: https://cmu.zoom.us/j/621951121 [cmu.zoom.us]
Meeting ID: 621 951 121
TITLE: Ulam stability for quotients of abelian non-archimedean Polish
groups
ABSTRACT: Based on an earlier work of Shelah concerning the relationship
of the continuum hypothesis to the cardinality of the set of automorphisms
of $\mathcal{P}(\omega)/\mathrm{fin}$, Velickovic showed that if such an
automorphism admits a Borel lift $\mathcal{P}(\omega)\to
\mathcal{P}(\omega)$, then it is of a certain "trivial" form. Similarly,
Kanovei and Reeken showed that if $N,M$ are countable dense subgroups of
$\mathbb{R}$, then every homomorphism $\mathbb{R}/N\to \mathbb{R}/M$ with
a Borel lift $\mathbb{R}\to \mathbb{R}$, is of a certain "trivial" form.
Kanovei and Reeken asked whether quotients of the $p$-adic groups satisfy
similar "Ulam stability" phenomena. In this talk, we will settle this
question by providing Ulam-stability phenomena for definable homomorphisms
$G/N\to H/M$ when $G,H$ are arbitrary abelian non-archimedean Polish
groups and $N,M$ are Polishable subgroups. We will then illustrate how
such rigidity results are in the heart of the definable cohomology theory
which we developed in the previous talk.
This is joint work with Jeffrey Bergfalk and Martino Lupini.
THURSDAY, February 25, 2021
Model Theory Seminar: 10:00 A.M., Online, Michael Lieberman, Brno
University of Technology
Join Zoom Meeting:
https://cmu.zoom.us/j/96301869290?pwd=Qk1zS0h6ZThmUnRpbmNLNkVJSjkrQT09
Meeting ID: 963 0186 9290
Passcode: 567655
TITLE: Induced and higher-dimensional stable independence, Part I
ABSTRACT: We introduce the notion of a stable independence relation on an
abstract category, generalizing the notions familiar from classical and
abstract model theory. We discuss certain useful properties of such
relations---chiefly, canonicity---and indicate that, in mu-AECs, the
existence of a stable independence notion has the expected relationship
with the failure of the order property.
We highlight an important special case, in which the category is derived
by restricting to a nice family of morphisms in a larger, locally
presentable category (e.g. R-modules with pure homomorphisms). Here we
find a surprisingly deep connection between the existence of a stable
independence notion and the structure of the family of morphisms. Joint
work with J. Rosický and S. Vasey.
TUESDAY, March 2, 2021
Mathematical logic seminar: 3:30 P.M., Online, Marc Noy, Technical
University of Catalonia
Join Zoom Meeting: https://cmu.zoom.us/j/621951121 [cmu.zoom.us]
Meeting ID: 621 951 121
TITLE: Zero-One and Convergence Laws for Graphs Embeddable on a Fixed
Surface
ABSTRACT: Let G be a class of labeled graphs with the uniform probability
distribution on graphs with a fixed number of vertices. Given a graph
property A, we are interested in the limiting probability that A holds in
G. It was shown by Heinig et al. that this limiting probability always
exists when G is the class of planar graphs and A is any property
expressible in monadic second order logic (MSO), and it was conjectured
that the same result holds for the class of graphs embeddable on a fixed
surface S. After reviewing the results for planar graphs, and more
generally for minor-closed classes of graphs, we will refute the
conjecture by showing that for every closed surface (orientable or not)
other than the sphere there exists an MSO graph property whose limiting
probability does not exist. In addition we show that every rational number
in [0,1] is the limiting probability of some MSO property, as opposed to
the class of planar graphs where there are so-called gaps. The proof
relies on a combination of methods from structural graph theory,
concretely large face-width embeddings of graphs on surfaces, analytic
combinatorics, and finite model theory.
This is joint work with Albert Atserias and Stephan Kreutzer.
THURSDAY, March 4, 2021
Model Theory Seminar: 10:00 A.M., Online, Michael Lieberman, Brno
University of Technology
Join Zoom Meeting:
https://cmu.zoom.us/j/96301869290?pwd=Qk1zS0h6ZThmUnRpbmNLNkVJSjkrQT09
Meeting ID: 963 0186 9290
Passcode: 567655
TITLE: Induced and higher-dimensional stable independence, Part II
ABSTRACT: We discuss the conditions under which a stable independence
relation can be pushed upward---induced---from a subcategory to the
category as a whole: namely, that the larger category is weakly stable and
the subcategory is sufficiently nicely embedded. While a model-theoretic
argument can be given, we suggest that the category-theoretic analog is
cleaner and more efficient.
This has immediate applications: the algebraic classes considered in
recent work of Mazari-Armida (torsion R-modules with pure monomorphisms,
torsion-free Abelian groups with pure embeddings, etc.) all have
weakly-stable independence notions. Thanks to Mazari-Armida's results on
Galois stability of such classes (and a few additional properties), it is
clear that in each case the subcategory of sufficiently saturated objects
has a stable independence notion: we conclude that the same holds of the
categories themselves.
Time permitting, we will also discuss the phenomenon of excellence---that
is, the existence of stable independence in all dimensions---in this
context. As it happens, in any category of the special form considered in
Part I (obtained by restricting to a nice class of morphisms in a nice
category), excellence follows directly from the existence of a stable
independence notion. Joint work with J. Rosický and S. Vasey.
TUESDAY, April 20, 2021
Mathematical logic seminar: 3:30 P.M., Online, Sandra Müller, University
of Vienna
Join Zoom Meeting: https://cmu.zoom.us/j/621951121 [cmu.zoom.us]
Meeting ID: 621 951 121
TITLE: TBA
TUESDAY, April 20, 2021
Set Theory Reading Group: 4:30 P.M., Online, Sandra Müller, University of
Vienna
Join Zoom Meeting: https://cmu.zoom.us/j/621951121 [cmu.zoom.us]
Meeting ID: 621 951 121
TITLE: TBA
This Week in Logic at CUNY
This Week in Logic at CUNY
2/7/2021 20:00:00
This Week in Logic at CUNY:
- - - - Monday, Feb 8, 2021 - - - -
Logic and Metaphysics Workshop
Date: Monday, Feb 8, 4.15-6.15 (NY time)
For meeting information, please email: yweiss@gradcenter.cuny.edu Patrick Girard, AucklandTitle: Classical Counterpossibles
Abstract: We present four classical theories of counterpossibles that combine modalities and counterfactuals. Two theories are anti-vacuist and forbid vacuously true counterfactuals, two are quasi-vacuist and allow counterfactuals to be vacuously true when their antecedent is not only impossible, but also inconceivable. The theories vary on how they restrict the interaction of modalities and counterfactuals. We provide a logical cartography with precise acceptable boundaries, illustrating to what extent nonvacuism about counterpossibles can be reconciled with classical logic.
Note: this is joint work with Rohan French (UC Davis) and Dave Ripley (Monash).
- - - - Tuesday, Feb 9, 2021 - - - -
Models of Peano Arithmetic (MOPA)
Tuesday, Feb 9, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. Leszek Kołodziejczyk, University of Warsaw
An isomorphism theorem for models of Weak Kőnig's Lemma without induction
We prove that any two countable models of the theory WKL∗0WKL0∗ sharing the same first-order universe and containing the same counterexample to Σ01Σ10 induction are isomorphic.
This theorem implies that over WKL∗0+¬IΣ01WKL0∗+¬IΣ10, the analytic hierarchy collapses to the arithmetic hierarchy. It also implies that WKL∗0WKL0∗ is the strongest Π12Π21 statement that is Π11Π11-conservative over RCA∗0+¬IΣ01RCA0∗+¬IΣ10. Together with the (slightly subtle) generalizations of the theorem to higher levels of the arithmetic hierarchy, this gives an 'almost negative' answer to a question of Towsner, who asked whether Π11Π11-conservativity of Π12Π21 sentences over collection principles is a Π02Π20-complete computational problem. Our results also have some implications for the reverse mathematics of combinatorial principles: for instance, we get a specific Π11Π11 sentence that is provable in RCA0+BΣ02RCA0+BΣ20 exactly if the Π11Π11 consequences of RCA0+RT22RCA0+RT22 coincide with BΣ02BΣ20.
On the side, we also give a positive answer to Towsner's question as originally stated.
Joint work with Marta Fiori Carones, Tin Lok Wong, and Keita Yokoyama.
- - - - Wednesday, Feb 10, 2021 - - - -
The New York City Category Theory Seminar
Speaker: Peter Hines University of York.
Date and Time: Wednesday February 10, 2021, 7:00 - 8:30 PM., on Zoom.
Title: Shuffling cards as an operad.
Abstract: The theory of how two packs of cards may be shuffled together to form a single pack has been remarkably well-studied in combinatorics, group theory, statistics, and other areas of mathematics. This talk aims to study natural extensions where 1/ We may have infinitely many cards in a deck, 2/ We may take the result of a previous shuffle as one of our decks of cards (i.e. shuffles are hierarchical), and 3/ There may even be an infinite number of decks of cards.
Far from being 'generalisation for generalisation's sake', the original motivation came from theoretical & practical computer science. The mathematics of card shuffles is commonly used to describe processing in multi-threaded computations. Moving to the infinite case gives a language in which one may talk about potentially non-terminating processes, or servers with an unbounded number of clients, etc.
However, this talk is entirely about algebra & category theory -- just as in the finite case, the mathematics is of interest in its own right, and should be studied as such.
We model shuffles using operads. The intuition behind them of allowing for arbitrary n-ary operations that compose in a hierarchical manner makes them a natural, inevitable choice for describing such processes such as merging multiple packs of cards.
We use very concrete examples, based on endomorphism operads in groupoids of arithmetic operations. The resulting structures are at the same time both simple (i.e. elementary arithmetic operations), and related to deep structures in mathematics and category theory (topologies, tensors, coherence, associahedra, etc.)
We treat this as a feature, not a bug, and use it to describe complex structures in elementary terms. We also aim to give previously unobserved connections between distinct areas of mathematics.
- - - - Thursday, Feb 11, 2021 - - - -
Philog Seminar
Thursday February 11, 6:30 PM
A Zoom link will be posted on philog.arthurpaulpedersen.org
Jayant Shah, Mathematics Department, Northeastern University
The Aumann Maschler paper on the Game theoretic analysis of a bankruptcy problem from the Talmud
- - - - Friday, Feb 12, 2021 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, Feb 12, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. Indestructibility (or otherwise) of subcompactness and C(n)-supercompactness
Indestructibility results of large cardinals have been an area of interest since Laver's 1978 proof that the supercompactness of κκ may be made indestructible by any <κ<κ-directed closed forcing. I will present a continuation of this work, showing that αα-subcompact cardinals may be made suitably indestructible, but that for C(n)-supercompact cardinals this is largely not possible.
Next Week in Logic at CUNY:
- - - - Monday, Feb 15, 2021 - - - -
- - - - Tuesday, Feb 16, 2021 - - - -
Models of Peano Arithmetic (MOPA)
Tuesday, Feb 16, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. Mateusz Łełyk, University of Warsaw
Nonequivalent axiomatizations of PAPA and the Tarski Boundary
We study a family of axioms expressing‘All axioms of PA are true.' (*)‘All axioms of PA are true.' (*)where PA denotes Peano Arithmetic. More precisely, each such axiom states that all axioms from a chosen axiomatization of PA are true. We start with a very natural theory of truth CT−(PA)CT−(PA) which is a finite extension of PA in the language of arithmetic augmented with a fresh predicate T to serve as a truth predicate for the language of arithmetic. Additional axioms of this theory are straightforward translations of inductive Tarski truth conditions. To study various possible ways of expressing (*), we investigate extensions of CT−(PA)CT−(PA) with axioms of the form∀x(δ(x)→T(x)).∀x(δ(x)→T(x)).In the above (and throughout the whole abstract) δ(x)δ(x) is an elementary formula which is proof-theoretically equivalent to the standard axiomatization of PA with the induction scheme, i.e. the equivalence∀x(Provδ(x)≡ProvPA(x)).∀x(Provδ(x)≡ProvPA(x)).is provable in IΣ1IΣ1. For every such δδ, the extension of CT−(PA)CT−(PA) with the above axiom will be denoted CT−[δ]CT−[δ].
In particular we shall focus on the arithmetical strength of theories CT−[δ]CT−[δ]. The 'line' demarcating extensions of CT−(PA)CT−(PA) which are conservative over PA from the nonconservative ones is known in the literature as the Tarski Boundary. For some time, there seemed to be the least (in terms of deductive strength) *natural* extension of CT−(PA)CT−(PA) on the nonconservative side of the boundary, whose one axiomatization is given by CT−(PA)CT−(PA) and Δ0Δ0 induction for the extended language (the theory is called CT0CT0). This theory can equivalently be axiomatized by adding to CT−(PA)CT−(PA) the natural formal representation of the statement 'All theorems of PAPA are true.'. We show that the situation between the Tarski Boundary and CT0CT0 is much more interesting:
Theorem 1: For every r.e. theory Th in the language of arithmetic the following are equivalent:
1) CT0⊢CT0⊢ Th
2) there exists δδ such that CT−[δ]CT−[δ] and Th have the same arithmetical consequences.
Theorem 1 can be seen as a representation theorem for r.e. theories below REFω(PA)REFω(PA) (all finite iterations of uniform reflection over PAPA, which is the set of arithmetical consequences of CT0CT0): each such theory can be finitely axiomatized by a theory of the form CT−[δ]CT−[δ], where δδ is proof-theoretically reducible to PAPA.
Secondly, we use theories CT−[δ]CT−[δ] to investigate the situation below the Tarski Boundary. We shall prove the following result
Theorem 2: There exists a family {δf}f∈ω<ω{δf}f∈ω<ω such that for all f,g∈ω<ωf,g∈ω<ω
1) CT−[δf]CT−[δf] is conservative over PAPA;
2) if f⊊gf⊊g, then CT−[δg]CT−[δg] properly extends CT−[δf]CT−[δf];
3) if f⊥gf⊥g then CT−[δg]∪CT−[δf]CT−[δg]∪CT−[δf] is nonconservative over PAPA (but consistent).
- - - - Wednesday, Feb 17, 2021 - - - -
The New York City Category Theory Seminar
Speaker: Richard Blute, University of Ottawa.
Date and Time: Wednesday February 17, 2021, 7:00 - 8:30 PM., on Zoom.
Title: Finiteness Spaces, Generalized Polynomial Rings and Topological Groupoids.
Abstract: The category of finiteness spaces was introduced by Thomas Ehrhard as a model of classical linear logic, where a set is equipped with a class of subsets to be thought of as finitary. Morphisms are relations preserving the finitary structure. The notion of finitary subset allows for a sharp analysis of computational structure.
Working with finiteness spaces forces the number of summands in certain calculations to be finite and thus avoid convergence questions. An excellent example of this is how Ribenboim’s theory of generalized power series rings can be naturally interpreted by assigning finiteness monoid structure to his partially ordered monoids. After Ehrhard’s linearization construction is applied, the resulting structures are the rings of Ribenboim’s construction.
There are several possible choices of morphism between finiteness spaces. If one takes structure-preserving partial functions, the resulting category is complete, cocomplete and symmetric monoidal closed. Using partial functions, we are able to model topological groupoids, when we consider composition as a partial function. We can associate to any hemicompact etale Hausdorff groupoid a complete convolution ring. This is in particular the case for the infinite paths groupoid associated to any countable row-finite directed graph.
- - - - Thursday, Feb 18, 2021 - - - -
- - - - Friday, Feb 19, 2021 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, Feb 19, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. Philipp Lücke, University of Bonn
TBA
- - - - Other Logic News - - - -
- - - - Web Site - - - -
"Find us on the web at:
nylogic.github.io(site designed, built & maintained by Victoria Gitman)"
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Barcelona Set theory Seminar
Barcelona Logic Seminar
2/7/2021 15:20:59
Dear All,
Please find attached the announcement of the next session of the Barcelona Set Theory Seminar. Feel free to distribute it.
SPEAKER: Matteo Viale (Università di Torino)
TITLE: The model-companionship spectrum of set theory, generic absoluteness, and the continuum problem.
TIME: February 10 at 16:00 (CET)
PLACE: The Seminar will take place online at the following address:
Best regards,
Joan
P.S.: If you do not wish to receive any more announcements, please send an email to
bagaria@ub.edu with the text “Unsubscribe”.
Joan Bagaria
ICREA Research Professor
Universitat de Barcelona
Departament de Matemàtiques i Informàtica
Gran Via de les Corts Catalanes 585
08007 Barcelona
Catalonia
Phone: +34 93 402 1609
Joan Bagaria
ICREA Research Professor
Universitat de Barcelona
Departament de Matemàtiques i Informàtica
Gran Via de les Corts Catalanes 585
08007 Barcelona
Catalonia
Phone: +34 93 402 1609
Talk by Andrés Villaveces tomorrow (1 30 pm)
Toronto Set Theory Seminar
2/4/2021 14:30:00
Hello everyone,
Please use the following link and fill the form (every week) to
enter the meeting. This form helps the Field Institute to know
statistical data about attendance.
Here the speaker information:
Speaker :Andrés Villaveces, Universidad Nacional de Colombia
Date and Time: Friday, February 5, 2021 - 1:30pm to 3:00pm
Title: Axiomatizations of abstract elementary classes and natural logics for model theory: the role of partition relations.
Abstract:
Two
seemingly unrelated questions (the quest for natural logics of abstract
elementary classes on the one hand, and the quest for logics adequate
to model theory on the other hand) converge around the same
combinatorial core: partition relations for scattered order types (due
to Kómjath and Shelah). I will present recent results concerning the
first question (and axiomatizing a.e.c.'s - joint work with Shelah) and
the second question (joint work with Väänänen).
Bio: Andrés Villaveces is a mathematician, working at Universidad
Nacional de Colombia in Bogotá. Villaveces earned his doctoral degree
from the University of Wisconsin-Madison in 1996 under the supervision
of Ken Kunen. He held a postdoctoral position at the Hebrew University
of Jerusalem (1996-1997) and has been a visiting professor at Carnegie
Mellon University (2002-2003) and at the University of Helsinki (2007
and 2015). His work centers on the model theory of Abstract Elementary
Classes and its connections with set theory and other parts of logic and
mathematics.
Iván Ongay Valverde (he/his)
Talk by Andrés Villaveces Friday ( 1 30 pm)
Toronto Set Theory Seminar
2/2/2021 15:51:33
Hello everyone,
Please use the following link and fill the form (every week) to
enter the meeting. This form helps the Field Institute to know
statistical data about attendance.
Here the speaker information:
Speaker :Andrés Villaveces, Universidad Nacional de Colombia
Date and Time: Friday, February 5, 2021 - 1:30pm to 3:00pm
Title: Axiomatizations of abstract elementary classes and natural logics for model theory: the role of partition relations.
Abstract:
Two
seemingly unrelated questions (the quest for natural logics of abstract
elementary classes on the one hand, and the quest for logics adequate
to model theory on the other hand) converge around the same
combinatorial core: partition relations for scattered order types (due
to Kómjath and Shelah). I will present recent results concerning the
first question (and axiomatizing a.e.c.'s - joint work with Shelah) and
the second question (joint work with Väänänen).
Bio: Andrés Villaveces is a mathematician, working at Universidad
Nacional de Colombia in Bogotá. Villaveces earned his doctoral degree
from the University of Wisconsin-Madison in 1996 under the supervision
of Ken Kunen. He held a postdoctoral position at the Hebrew University
of Jerusalem (1996-1997) and has been a visiting professor at Carnegie
Mellon University (2002-2003) and at the University of Helsinki (2007
and 2015). His work centers on the model theory of Abstract Elementary
Classes and its connections with set theory and other parts of logic and
mathematics.
Iván Ongay Valverde (he/his)
This Week in Logic at CUNY
This Week in Logic at CUNY
1/31/2021 18:36:05
This Week in Logic at CUNY:
- - - - Monday, Feb 1, 2021 - - - -
- - - - Tuesday, Feb 2, 2021 - - - -
Models of Peano Arithmetic (MOPA)
Wednesday, Feb 2, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. James Walsh, Cornell University
Reducing omega-model reflection to iterated syntactic reflection
Two types of principles are commonly called “reflection principles” in reverse mathematics. According to syntactic reflection principles for T, every theorem of T (from some complexity class) is true. According to semantic reflection principles, every set belongs to some (sufficiently correct) model of T. We will present a connection between syntactic reflection and semantic reflection in second-order arithmetic: for any Pi^1_2 axiomatized theory T, every set is contained in an omega model of T if and only if every iteration of Pi^1_1 reflection for T along a well-ordering is Pi^1_1 sound. There is a thorough proof-theoretic understanding of the latter in terms of ordinal analysis. Accordingly, these reductions yield proof-theoretic analyses of omega-model reflection principles. This is joint work with Fedor Pakhomov.
- - - - Wednesday, Feb 3, 2021 - - - -
The New York City Category Theory Seminar
Speaker: Jason Parker, Brandon University in Manitoba.
Date and Time: Wednesday February 3, 2021, 7:00 - 8:30 PM., on Zoom.
Title: Isotropy Groups of Quasi-Equational Theories.
Abstract: In [2], my PhD supervisors (Pieter Hofstra and Philip Scott) and I studied the new topos-theoretic phenomenon of isotropy (as introduced in [1]) in the context of single-sorted algebraic theories, and we gave a logical/syntactic characterization of the isotropy group of any such theory, thereby showing that it encodes a notion of inner automorphism or conjugation for the theory. In the present talk, I will summarize the results of my recent PhD thesis, in which I build on this earlier work by studying the isotropy groups of (multi-sorted) quasi-equational theories (also known as essentially algebraic, cartesian, or finite limit theories). In particular, I will show how to give a logical/syntactic characterization of the isotropy group of any such theory, and that it encodes a notion of inner automorphism or conjugation for the theory. I will also describe how I have used this characterization to exactly characterize the ‘inner automorphisms’ for several different examples of quasi-equational theories, most notably the theory of strict monoidal categories and the theory of presheaves valued in a category of models. In particular, the latter example provides a characterization of the (covariant) isotropy group of a category of set-valued presheaves, which had been an open question in the theory of categorical isotropy.
[1] J. Funk, P. Hofstra, B. Steinberg. Isotropy and crossed toposes. Theory and Applications of Categories 26, 660-709, 2012.
[2] P. Hofstra, J. Parker, P.J. Scott. Isotropy of algebraic theories. Electronic Notes in Theoretical Computer Science 341, 201-217, 2018.
- - - - Thursday, Feb 4, 2021 - - - -
- - - - Friday, Feb 5, 2021 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, Feb 5, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. Andreas Blass, University of Michigan
Choice from Finite Sets: A Topos View
Tarski proved (but didn't publish) the theorem that choice from pairs implies choice from four-element sets. Mostowski (1937) began a systematic study of such implications between choice axioms for families of finite sets. Gauntt (1970) completed that study (but didn't publish the results), obtaining equivalent characterizations in terms of fixed points of permutation groups. Truss (1973) extended Gauntt's results (and published this work).
It turns out that these finite choice axioms and their group-theoretic characterizations are instances of the same topos-theoretic statements, interpreted in two very different classes of topoi. My main result is an extension of that observation to the class of all topoi.
Most of my talk will be explaining the background: finite choice axioms, permutation groups, and a little bit about topoi - just enough to make sense of the main result. If time permits, I'll describe some of the ingredients of the proof.
Next Week in Logic at CUNY:
- - - - Monday, Feb 8, 2021 - - - -
Logic and Metaphysics Workshop
Date: Monday, Feb 8, 4.15-6.15 (NY time)
For meeting information, please email: yweiss@gradcenter.cuny.edu Patrick Girard, Auckland- - - - Tuesday, Feb 9, 2021 - - - -
Models of Peano Arithmetic (MOPA)
Wednesday, Feb 9, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. Leszek Kołodziejczyk, University of Warsaw
An isomorphism theorem for models of Weak Kőnig's Lemma without induction
We prove that any two countable models of the theory WKL∗0WKL0∗ sharing the same first-order universe and containing the same counterexample to Σ01Σ10 induction are isomorphic.
This theorem implies that over WKL∗0+¬IΣ01WKL0∗+¬IΣ10, the analytic hierarchy collapses to the arithmetic hierarchy. It also implies that WKL∗0WKL0∗ is the strongest Π12Π21 statement that is Π11Π11-conservative over RCA∗0+¬IΣ01RCA0∗+¬IΣ10. Together with the (slightly subtle) generalizations of the theorem to higher levels of the arithmetic hierarchy, this gives an 'almost negative' answer to a question of Towsner, who asked whether Π11Π11-conservativity of Π12Π21 sentences over collection principles is a Π02Π20-complete computational problem. Our results also have some implications for the reverse mathematics of combinatorial principles: for instance, we get a specific Π11Π11 sentence that is provable in RCA0+BΣ02RCA0+BΣ20 exactly if the Π11Π11 consequences of RCA0+RT22RCA0+RT22 coincide with BΣ02BΣ20.
On the side, we also give a positive answer to Towsner's question as originally stated.
Joint work with Marta Fiori Carones, Tin Lok Wong, and Keita Yokoyama.
- - - - Wednesday, Feb 10, 2021 - - - -
The New York City Category Theory Seminar
Speaker: Peter Hines University of York.
Date and Time: Wednesday February 10, 2021, 7:00 - 8:30 PM., on Zoom.
Title: Invertibility in Operads : an elementary arithmetic approach.
Abstract: This talk is motivated by two areas of 'lost mathematics' -- topics where it is clear that interesting theory was once known & understood, but only incomplete traces remain in the historical record. One of these was due to ancient Greek mathematicians & logicians, and the other is a much lesser-known relation of a famous open problem from the 20th century.
One objective of this talk is to trace a link between the two. However, this is not an exercise in the 'History of Mathematics' -- the connections rely on theory that certainly was not understood in either time period.
Precisely, we consider 'Invertible Operads' -- that is, those whose composition operations are either partially or globally invertible. We look at examples that are freely generated by some given set of operations, with particular reference to those whose composition operations may be given by elementary arithmetic functions.
We demonstrate how such structures arise in a range of different topics, providing previously unobserved connections between them. This includes subjects such as standard Young tableaux, mixed-radix counting systems, topologies on the natural numbers, logical models, famous groups, and combinatorially-inspired polyhedra.
This is very much work in progress, and aims to present interesting questions as much as interesting structures and results.
- - - - Thursday, Feb 11, 2021 - - - -
- - - - Friday, Feb 12, 2021 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, Feb 12, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. Bea Adam-Day, University of Leeds
- - - - Other Logic News - - - -
- - - - Web Site - - - -
"Find us on the web at:
nylogic.github.io(site designed, built & maintained by Victoria Gitman)"
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to
jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email
jreitz@nylogic.org.
Barcelona Set theory Seminar
Barcelona Logic Seminar
1/31/2021 17:02:10
Dear All,
Please find attached the announcement of the next session of the Barcelona Set Theory Seminar. Feel free to distribute it.
SPEAKER: Adrian Mathias (Université de la Réunion)
TITLE: Power-admissible sets and ill-founded omega-models of weak subsystems of ZFC
TIME: February 3 at 16:00 (CET)
PLACE: The Seminar will take place online at the following address:
Best regards,
Joan
P.S.: If you do not wish to receive any more announcements, please send an email to
bagaria@ub.edu with the text “Unsubscribe”.
Joan Bagaria
ICREA Research Professor
Universitat de Barcelona
Departament de Matemàtiques i Informàtica
Gran Via de les Corts Catalanes 585
08007 Barcelona
Catalonia
Phone: +34 93 402 1609
CMU events starting next week
Carnegie Mellon Logic Seminar
1/29/2021 21:30:55
TUESDAY, February 2, 2021
Mathematical logic seminar: 3:30 P.M., Online, Anush Tserunyan, McGill
University
Join Zoom Meeting: https://cmu.zoom.us/j/621951121 [cmu.zoom.us]
Meeting ID: 621 951 121
TITLE: Ergodic theorems along trees
ABSTRACT: In the classical pointwise ergodic theorem for a probability
measure preserving (pmp) transformation $T$, one takes averages of a given
integrable function over the intervals $\{x, T(x), T^2(x), \hdots,
T^n(x)\}$ in front of the point $x$. We prove a “backward” ergodic theorem
for a countable-to-one pmp $T$, where the averages are taken over subtrees
of the graph of T that are rooted at $x$ and lie behind $x$ (in the
direction of $T^{-1}$). Surprisingly, this theorem yields forward ergodic
theorems for countable groups, in particular, one for pmp actions of free
groups of finite rank, where the averages are taken along subtrees of the
standard Cayley graph rooted at the identity. This strengthens Bufetov’s
theorem from 2000, which was the most general result in this vein. This is
joint work with Jenna Zomback.
TUESDAY, February 2, 2021
Set Theory Reading Group: 4:30 P.M., Online, Jenna Zomback, University of
Illinois at Urbana-Champaign
Join Zoom Meeting: https://cmu.zoom.us/j/621951121 [cmu.zoom.us]
Meeting ID: 621 951 121
TITLE: Ergodic theorems along trees: the proofs
ABSTRACT: In this continuation of the previous talk, we discuss a backward
(inverse) ergodic theorem for a probability measure preserving (pmp)
transformation $T$, where the averages are taken over subtrees of the
graph of $T$ that are rooted at $x$ and lie behind $x$ (in the direction
of $T^{-1}$). We will derive from it a new (forward) pointwise ergodic
theorem for pmp actions of free groups of finite rank, where the averages
are taken along subtrees of the standard Cayley graph rooted at the
identity. We will then discuss a very short proof (due to Tserunyan) of
the classical pointwise ergodic theorem, and, using this proof as an
outline, we will sketch the proof of the backward ergodic theorem. This is
joint work with Anush Tserunyan.
THURSDAY, February 4, 2021
Model Theory Seminar: 10:00 A.M., Online, John Baldwin, UIC
Join Zoom Meeting:
https://cmu.zoom.us/j/96301869290?pwd=Qk1zS0h6ZThmUnRpbmNLNkVJSjkrQT09
Meeting ID: 963 0186 9290
Passcode: 567655
TITLE: The Hanf number for extendability is the first measurable cardinal,
Part 1
ABSTRACT: We prove in ZFC the existence of a complete sentence of
infinitary logic that has maximal models in a set of cardinals cofinal in
the first measurable but no maximal models in any cardinal beyond the
first measurable. As a warmup to the first lecture please look at the
Motivation http://homepages.math.uic.edu/~jbaldwin/pub/cmupre
This is joint work with Saharon Shelah.
Preprints are available at
http://homepages.math.uic.edu/~jbaldwin/pub/ahanfmaxjan21.pdf and
http://homepages.math.uic.edu/~jbaldwin/pub/ahazfjan7.pdf
TUESDAY, February 9, 2021
Mathematical logic seminar: 3:30 P.M., Online, Benjamin Siskind,
University of California, Berkeley
Join Zoom Meeting: https://cmu.zoom.us/j/621951121 [cmu.zoom.us]
Meeting ID: 621 951 121
TITLE: Order-preserving Martin’s Conjecture
ABSTRACT: Martin’s Conjecture is a precise way of asserting that, up to
equivalence, the only natural functions on the Turing degrees are the
familiar ones: the constant functions, the identity, the Turing jump, and
the transfinite iterates of the Turing jump. This conjecture is open even
restricted to low-level Borel functions, but there have been partial
results over the years which show it holds for classes of functions
meeting requirements orthogonal to definability. Our recent result is that
part of Martin’s Conjecture (lately called “part one”) holds for the class
of order-preserving functions. In particular, it follows that the full
Martin’s Conjecture holds for Borel order-preserving functions. We’ll talk
about Martin’s Conjecture broadly and say something about this recent
work. This is joint work with Patrick Lutz.
TUESDAY, February 9, 2021
Set Theory Reading Group: 4:30 P.M., Online, Benjamin Siskind, University
of California, Berkeley
Join Zoom Meeting: https://cmu.zoom.us/j/621951121 [cmu.zoom.us]
Meeting ID: 621 951 121
TITLE: Measure-preserving functions on the Turing degrees
ABSTRACT: One proof of part one of Martin’s Conjecture for
order-preserving functions works for a bigger class of functions: those
which are measure-preserving for the Martin measure, in the sense of
ergodic theory. Looking at this class of functions brings out more
set-theoretic aspects of Martin’s Conjecture. For example, part one of
Martin’s Conjecture is equivalent to the non-existence of other
non-principal ultrafilters on the Turing degrees Rudin-Keisler below the
Martin measure. We’ll talk about the proof of part one of Martin’s
Conjecture for this class of functions and some consequences. This is
joint work with Patrick Lutz.
THURSDAY, February 11, 2021
Model Theory Seminar: 10:00 A.M., Online, John Baldwin, UIC
Join Zoom Meeting:
https://cmu.zoom.us/j/96301869290?pwd=Qk1zS0h6ZThmUnRpbmNLNkVJSjkrQT09
Meeting ID: 963 0186 9290
Passcode: 567655
TITLE: The Hanf number for extendability is the first measurable cardinal,
Part 2
ABSTRACT: We prove in ZFC the existence of a complete sentence of
infinitary logic that has maximal models in a set of cardinals cofinal in
the first measurable but no maximal models in any cardinal beyond the
first measurable. As a warmup to the first lecture please look at the
Motivation http://homepages.math.uic.edu/~jbaldwin/pub/cmupre
This is joint work with Saharon Shelah.
Preprints are available at
http://homepages.math.uic.edu/~jbaldwin/pub/ahanfmaxjan21.pdf and
http://homepages.math.uic.edu/~jbaldwin/pub/ahazfjan7.pdf
TUESDAY, February 16, 2021
Mathematical logic seminar: 3:30 P.M., Online, Aristotelis
Panagiotopoulos, University of Muenster
Join Zoom Meeting: https://cmu.zoom.us/j/621951121 [cmu.zoom.us]
Meeting ID: 621 951 121
TITLE: The definable content of (co)homological invariants: Cech
cohomology
ABSTRACT: In this talk we will develop a framework for enriching various
classical invariants of homological algebra and algebraic topology with
additional descriptive set-theoretic information. The resulting "definable
invariants" can be used for much finer classification than their purely
algebraic counterparts. We will then illustrate how these ideas apply to
the classical Cech cohomology theory, by introducing a new invariant for
locally compact metrizable spaces up to homotopy equivalence which we call
"definable cohomology". In strong contrast to its classical counterpart,
this definable cohomology theory provides complete classification to
homotopy classes of mapping telescopes of d-tori, and for homotopy classes
of maps from mapping telescopes of d-tori to spheres. The latter problem
was raised in the d=1 case by Borsuk and Eilenberg in 1936.
This is joint work with Jeffrey Bergfalk and Martino Lupini.
TUESDAY, February 16, 2021
Set Theory Reading Group: 4:30 P.M., Online, Aristotelis Panagiotopoulos,
University of Muenster
Join Zoom Meeting: https://cmu.zoom.us/j/621951121 [cmu.zoom.us]
Meeting ID: 621 951 121
TITLE: Ulam stability for quotients of abelian non-archimedean Polish
groups
ABSTRACT: Based on an earlier work of Shelah concerning the relationship
of the continuum hypothesis to the cardinality of the set of automorphisms
of $\mathcal{P}(\omega)/\mathrm{fin}$, Velickovic showed that if such an
automorphism admits a Borel lift $\mathcal{P}(\omega)\to
\mathcal{P}(\omega)$, then it is of a certain "trivial" form. Similarly,
Kanovei and Reeken showed that if $N,M$ are countable dense subgroups of
$\mathbb{R}$, then every homomorphism $\mathbb{R}/N\to \mathbb{R}/M$ with
a Borel lift $\mathbb{R}\to \mathbb{R}$, is of a certain "trivial" form.
Kanovei and Reeken asked whether quotients of the $p$-adic groups satisfy
similar "Ulam stability" phenomena. In this talk, we will settle this
question by providing Ulam-stability phenomena for definable homomorphisms
$G/N\to H/M$ when $G,H$ are arbitrary abelian non-archimedean Polish
groups and $N,M$ are Polishable subgroups. We will then illustrate how
such rigidity results are in the heart of the definable cohomology theory
which we developed in the previous talk.
This is joint work with Jeffrey Bergfalk and Martino Lupini.
TUESDAY, March 2, 2021
Mathematical logic seminar: 3:30 P.M., Online, Marc Noy, Technical
University of Catalonia
Join Zoom Meeting: https://cmu.zoom.us/j/621951121 [cmu.zoom.us]
Meeting ID: 621 951 121
TITLE: Zero-One and Convergence Laws for Graphs Embeddable on a Fixed
Surface
ABSTRACT: Let G be a class of labeled graphs with the uniform probability
distribution on graphs with a fixed number of vertices. Given a graph
property A, we are interested in the limiting probability that A holds in
G. It was shown by Heinig et al. that this limiting probability always
exists when G is the class of planar graphs and A is any property
expressible in monadic second order logic (MSO), and it was conjectured
that the same result holds for the class of graphs embeddable on a fixed
surface S. After reviewing the results for planar graphs, and more
generally for minor-closed classes of graphs, we will refute the
conjecture by showing that for every closed surface (orientable or not)
other than the sphere there exists an MSO graph property whose limiting
probability does not exist. In addition we show that every rational number
in [0,1] is the limiting probability of some MSO property, as opposed to
the class of planar graphs where there are so-called gaps. The proof
relies on a combination of methods from structural graph theory,
concretely large face-width embeddings of graphs on surfaces, analytic
combinatorics, and finite model theory.
This is joint work with Albert Atserias and Stephan Kreutzer.
TUESDAY, April 20, 2021
Mathematical logic seminar: 3:30 P.M., Online, Sandra Müller, University
of Vienna
Join Zoom Meeting: https://cmu.zoom.us/j/621951121 [cmu.zoom.us]
Meeting ID: 621 951 121
TITLE: TBA
TUESDAY, April 20, 2021
Set Theory Reading Group: 4:30 P.M., Online, Sandra Müller, University of
Vienna
Join Zoom Meeting: https://cmu.zoom.us/j/621951121 [cmu.zoom.us]
Meeting ID: 621 951 121
TITLE: TBA
Tomorrow: Corey Switzer at 1 30 pm (Toronto Time)
Toronto Set Theory Seminar
1/28/2021 13:01:00
Hello everyone,
Please use the following link and fill the form (every week) to
enter the meeting. This form helps the Field Institute to know
statistical data about attendance.
Here the speaker information:
Speaker: Corey Switzer, The Graduate Center, CUNY
Date and Time: Friday, January 29, 2021 - 1:30pm to 3:00pm (Toronto time)
Title: Higher Dimensional Cardinal Characteristics for Sets of Real Valued Functions
Abstract:
Cardinal characteristics on the generalized Baire
and Cantor spaces $\kappa^\kappa$ and $2^\kappa$ have recently generated
significant interest. In this talk I will introduce a different
generalization of cardinal characteristics, namely
to the space of functions $f:\omega^\omega \to \omega^\omega$. Given an
ideal $I$ on Baire space and a relation $R$ let us define $f R_I g$ for
$f$ and $g$ functions from $\omega^\omega$ to $\omega^\omega$ if and
only if $f(x) R g(x)$ for an $I$-measure one
set of $x \in \omega^\omega$. By letting $I$ vary over the null ideal,
the meager ideal and the bounded ideal; and $R$ vary over the relations
$\leq^*$, $\neq^*$ and
$\in^*$
we get 18 new cardinal characteristics by considering the bounding and
dominating numbers for these relations. These new cardinals form a
diagram of provable implications similar to the Cichoń diagram.
They also interact in several surprising ways with the cardinal
characteristics on $\omega$. For instance, they can be arbitrarily large
in models of CH, yet they can be
$\aleph_1$
in models where the continuum is arbitrarily large. They are bigger in
the Sacks model than the Cohen model. I will introduce these cardinals,
show some of the provable implications and discuss
what is known about consistent inequalities, focusing on the
$\mathfrak{b}$-numbers in well-known models such as the Cohen and Random
model. This is joint work with Jörg Brendle.
Bio: Corey Bacal Switzer is currently a postdoctoral researcher at
the Kurt Gödel Research Center For Mathematical Logic in the Mathematics
Department of the University of Vienna working under Vera Fischer. He
finished his PhD at the CUNY Graduate Center in New York in 2020. His
research is in set theory, focusing on forcing, cardinal characteristics
and infinite combinatorics
Iván Ongay Valverde (he/his)
Logic Seminar 3 Feb 2021 17:00 hrs at NUS by Wong Tin Lok
NUS Logic Seminar
1/28/2021 3:41:46
Invitation to the Logic Seminar at the National University of Singapore
Date: Wednesday, 3 February 2021, 17:00 hrs
Talk via Zoom: https://nus-sg.zoom.us/j/96860201432?pwd=cVdwZmd2clVFaEhaTmJjaGdXMFdmdz09
Meeting ID: 968 6020 1432
Password: Is P=NP?
Speaker: Wong Tin Lok
Title: Arithmetic under negated induction
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Abstract:
Arithmetic generally does not admit any non-trivial quantifier
elimination. I will talk about one exception, where the negation of
an induction axiom is included in the theory. Here the Weak Koenig's
Lemma from reverse mathematics arises as a model completion.
This work is joint with Marta Fiori-Carones, Leszek Aleksander Kolodziejczyk
and Keita Yokoyama.
Barcelona Set theory Seminar
Barcelona Logic Seminar
1/25/2021 11:50:42
Dear All,
Please find attached the announcement of the next session of the Barcelona Set Theory Seminar. Feel free to distribute it.
SPEAKER: Richard Matthews (Univ. of Leeds)
TITLE: Taking Reinhardt’s Power Away
TIME: January 27 at 16:00 (CET)
PLACE: The Seminar will take place online at the following address:
Best regards,
Joan
P.S.: If you do not wish to receive any more announcements, please send an email to
bagaria@ub.edu with the text “Unsubscribe”.
Joan Bagaria
ICREA Research Professor
Universitat de Barcelona
Departament de Matemàtiques i Informàtica
Gran Via de les Corts Catalanes 585
08007 Barcelona
Catalonia
Phone: +34 93 402 1609
Joan Bagaria
ICREA Research Professor
Universitat de Barcelona
Departament de Matemàtiques i Informàtica
Gran Via de les Corts Catalanes 585
08007 Barcelona
Catalonia
Phone: +34 93 402 1609
(KGRC) research seminar talk on Thursday, January 28
Kurt Godel Research Center
1/25/2021 11:33:35
Research seminar
Kurt Gödel Research Center
Thursday, January 28
"Distributivity spectrum of forcing notions"
Marlene Koelbing (KGRC), Wolfgang Wohofsky (KGRC)
In our talk, we will introduce two different notions of a spectrum of
distributivity of forcings.
The first one is the fresh function spectrum, which is the set of regular
cardinals lambda, such that the forcing adds a new function with domain lambda
all whose initial segments are in the ground model. We will provide several
examples as well as general facts how to compute the fresh function spectrum,
also discussing what sets are realizable as a fresh function spectrum of a
forcing.
The second notion is the combinatorial distributivity spectrum, which is the
set of possible regular heights of refining systems of maximal antichains
without common refinement. We discuss the relation between the fresh function
spectrum and the combinatorial distributivity spectrum. We consider the special
case of P(omega)/fin (for which h is the minimum of the spectrum), and use a
forcing construction to show that it is consistent that the combinatorial
distributivity spectrum of P(omega)/fin contains more than one element.
This is joint work with Vera Fischer.
Time and Place
Talk at 3:00pm via Zoom: This talk will be given via Zoom. If you have not
received the meeting link by the day before the talk, please contact
richard.springer@univie.ac.at!
This Friday Talk: Corey Switzer (usual time)
Toronto Set Theory Seminar
1/25/2021 9:03:43
Hello everyone,
Please use the following link and fill the form (every week) to
enter the meeting. This form helps the Field Institute to know
statistical data about attendance.
Here the speaker information:
Speaker: Corey Switzer, The Graduate Center, CUNY
Date and Time: Friday, January 29, 2021 - 1:30pm to 3:00pm
Title: Higher Dimensional Cardinal Characteristics for Sets of Real Valued Functions
Abstract:
Cardinal characteristics on the generalized Baire
and Cantor spaces $\kappa^\kappa$ and $2^\kappa$ have recently generated
significant interest. In this talk I will introduce a different
generalization of cardinal characteristics, namely
to the space of functions $f:\omega^\omega \to \omega^\omega$. Given an
ideal $I$ on Baire space and a relation $R$ let us define $f R_I g$ for
$f$ and $g$ functions from $\omega^\omega$ to $\omega^\omega$ if and
only if $f(x) R g(x)$ for an $I$-measure one
set of $x \in \omega^\omega$. By letting $I$ vary over the null ideal,
the meager ideal and the bounded ideal; and $R$ vary over the relations
$\leq^*$, $\neq^*$ and
$\in^*$
we get 18 new cardinal characteristics by considering the bounding and
dominating numbers for these relations. These new cardinals form a
diagram of provable implications similar to the Cichoń diagram.
They also interact in several surprising ways with the cardinal
characteristics on $\omega$. For instance, they can be arbitrarily large
in models of CH, yet they can be
$\aleph_1$
in models where the continuum is arbitrarily large. They are bigger in
the Sacks model than the Cohen model. I will introduce these cardinals,
show some of the provable implications and discuss
what is known about consistent inequalities, focusing on the
$\mathfrak{b}$-numbers in well-known models such as the Cohen and Random
model. This is joint work with Jörg Brendle.
Bio: Corey Bacal Switzer is currently a postdoctoral researcher at
the Kurt Gödel Research Center For Mathematical Logic in the Mathematics
Department of the University of Vienna working under Vera Fischer. He
finished his PhD at the CUNY Graduate Center in New York in 2020. His
research is in set theory, focusing on forcing, cardinal characteristics
and infinite combinatorics
Iván Ongay Valverde (he/his)
This Week in Logic at CUNY
This Week in Logic at CUNY
1/24/2021 19:10:35
This Week in Logic at CUNY:
- - - - Monday, Jan 25, 2021 - - - -
- - - - Tuesday, Jan 26, 2021 - - - -
- - - - Wednesday, Jan 27, 2021 - - - -
- - - - Thursday, Jan 28, 2021 - - - -
- - - - Friday, Jan 29, 2021 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, Jan 29, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. Erin Carmody, Fordham University
The relationships between measurable and strongly compact cardinals: Part II
This talk is about the ongoing investigation of the relationships between measurable and strongly compact cardinals. I will present some of the history of the theorems in this theme, including Magidor's identity crisis, and give new results. The theorems presented are in particular about the relationships between strongly compact cardinals and measurable cardinals of different Mitchell orders. One of the main theorems is that there is a universe where κ1κ1 and κ2κ2 are the first and second strongly compact cardinals, respectively, and where κ1κ1 is least with Mitchell order 1, and κ2κ2 is the least with Mitchell order 2. Another main theorem is that there is a universe where κ1κ1 and κ2κ2 are the first and second strongly compact cardinals, respectively, with κ1κ1 the least measurable cardinal such that o(κ1)=2o(κ1)=2 and κ2κ2 the least measurable cardinal above κ1κ1. This is a joint work in progress with Victoria Gitman and Arthur Apter.
Next Week in Logic at CUNY:
- - - - Monday, Feb 1, 2021 - - - -
- - - - Tuesday, Feb 2, 2021 - - - -
Models of Peano Arithmetic (MOPA)
Wednesday, Dec 9, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. James Walsh, Cornell University
Reducing omega-model reflection to iterated syntactic reflection
Two types of principles are commonly called “reflection principles” in reverse mathematics. According to syntactic reflection principles for T, every theorem of T (from some complexity class) is true. According to semantic reflection principles, every set belongs to some (sufficiently correct) model of T. We will present a connection between syntactic reflection and semantic reflection in second-order arithmetic: for any Pi^1_2 axiomatized theory T, every set is contained in an omega model of T if and only if every iteration of Pi^1_1 reflection for T along a well-ordering is Pi^1_1 sound. There is a thorough proof-theoretic understanding of the latter in terms of ordinal analysis. Accordingly, these reductions yield proof-theoretic analyses of omega-model reflection principles. This is joint work with Fedor Pakhomov.
- - - - Wednesday, Feb 3, 2021 - - - -
- - - - Thursday, Feb 4, 2021 - - - -
- - - - Friday, Feb 5, 2021 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, Feb 5, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. Andreas Blass, University of Michigan
TBA
- - - - Other Logic News - - - -
- - - - Web Site - - - -
"Find us on the web at:
nylogic.github.io(site designed, built & maintained by Victoria Gitman)"
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jreitz@nylogic.org.
Two talks by B. Siskind on February 9
Carnegie Mellon Logic Seminar
1/22/2021 21:22:24
TUESDAY, February 9, 2021
Mathematical logic seminar: 3:30 P.M., Online, Benjamin Siskind,
University of California, Berkeley
Join Zoom Meeting: https://cmu.zoom.us/j/621951121 [cmu.zoom.us]
Meeting ID: 621 951 121
TITLE: Order-preserving Martin’s Conjecture
ABSTRACT: Martin’s Conjecture is a precise way of asserting that, up to
equivalence, the only natural functions on the Turing degrees are the
familiar ones: the constant functions, the identity, the Turing jump, and
the transfinite iterates of the Turing jump. This conjecture is open even
restricted to low-level Borel functions, but there have been partial
results over the years which show it holds for classes of functions
meeting requirements orthogonal to definability. Our recent result is that
part of Martin’s Conjecture (lately called “part one”) holds for the class
of order-preserving functions. In particular, it follows that the full
Martin’s Conjecture holds for Borel order-preserving functions. We’ll talk
about Martin’s Conjecture broadly and say something about this recent
work. This is joint work with Patrick Lutz.
TUESDAY, February 9, 2021
Set Theory Reading Group: 4:30 P.M., Online, Benjamin Siskind, University
of California, Berkeley
Join Zoom Meeting: https://cmu.zoom.us/j/621951121 [cmu.zoom.us]
Meeting ID: 621 951 121
TITLE: Measure-preserving functions on the Turing degrees
ABSTRACT: One proof of part one of Martin’s Conjecture for
order-preserving functions works for a bigger class of functions: those
which are measure-preserving for the Martin measure, in the sense of
ergodic theory. Looking at this class of functions brings out more
set-theoretic aspects of Martin’s Conjecture. For example, part one of
Martin’s Conjecture is equivalent to the non-existence of other
non-principal ultrafilters on the Turing degrees Rudin-Keisler below the
Martin measure. We’ll talk about the proof of part one of Martin’s
Conjecture for this class of functions and some consequences. This is
joint work with Patrick Lutz.
Tomorrow two talks (11 am and 1 30 pm)
Toronto Set Theory Seminar
1/21/2021 12:00:00
Hello everyone,
To start the semester we will have two talks: one at 11 am (Toronto time) and another at 1 30 pm (Toronto time).
Please use the following link and fill the form (every week) to
enter the meeting. This form helps the Field Institute to know
statistical data about attendance.
Here the speakers information:
Speaker:Dima Sinapova, UIC, University of Illinois at Chicago, University of Illinois, Chicago
Date and Time: Friday, January 22, 2021 - 11am to 12:30pm
Title: Iteration, reflection, and singular cardinals
Abstract:
Two classical results of Magidor are: (1) from large cardinals it is consistent to have reflection at
$\aleph_{\omega+1}$ and (2) from large cardinals it is consistent to have the failure of SCH at $\aleph_{\omega}$.
These principles are at odds with each other. The former is a
compactness type principle. (Compactness is the phenomenon where if a
certain property holds for every smaller substructure of an object, then
it holds for the entire object.) In contrast, failure of SCH is an
instance of incompactness. The natural question is whether we can have
both of these simultaneously. We show the answer is yes.
We describe a Prikry style iteration, and use it to force stationary
reflection in the presence of not SCH. Then we obtain this situation at
$\aleph_{\omega}$
. This is joint work with Alejandro Poveda and Assaf Rinot.
Speaker: Marcos Mazari Armida, Carnagie Mellon University
Date and Time: Friday, January 22, 2021 - 1:30pm to 3pm
Title: Universal models in classes of abelian groups and modules
Abstract:
The search for universal models began in the early twentieth century
when Hausdorff showed that there is a universal linear order of
cardinality $\aleph_{n+1}$ if $2^{\aleph_n}= \aleph_{n + 1}$, i.e., a
linear order $U$ of cardinality $\aleph_{n+1}$ such that every linear
order of cardinality $\aleph_{n+1}$ embeds in $U$. In this talk, we will
study universal models in several classes of abelian groups and modules
with respect to pure embeddings. In particular, we will present a
complete solution below $\aleph_\omega$, with the exception of
$\aleph_0$ and $\aleph_1$, to Problem 5.1 in page 181 of \emph{Abelian
Groups} by L\'{a}szl\'{o} Fuchs, which asks to find the cardinals
$\lambda$ such that there is a universal abelian p-group for purity of
cardinality $\lambda$. The solution presented will use both
model-theoretic and set-theoretic ideas.
Iván Ongay Valverde (he/his)
Two events on February 16
Carnegie Mellon Logic Seminar
1/19/2021 13:27:45
TUESDAY, February 16, 2021
Mathematical logic seminar: 3:30 P.M., Online,
Aristotelis Panagiotopoulos, University of Muenster
Join Zoom Meeting: https://cmu.zoom.us/j/621951121 [cmu.zoom.us]
Meeting ID: 621 951 121
TITLE: The definable content of (co)homological invariants: Cech cohomology
ABSTRACT: In this talk we will develop a framework for enriching various
classical invariants of homological algebra and algebraic topology with
additional descriptive set-theoretic information. The resulting "definable
invariants" can be used for much finer classification than their purely
algebraic counterparts. We will then illustrate how these ideas apply to the
classical Cech cohomology theory, by introducing a new invariant for locally
compact metrizable spaces up to homotopy equivalence which we call "definable
cohomology". In strong contrast to its classical counterpart, this definable
cohomology theory provides complete classification to homotopy classes of
mapping telescopes of d-tori, and for homotopy classes of maps from mapping
telescopes of d-tori to spheres. The latter problem was raised in the d=1 case
by Borsuk and Eilenberg in 1936.
This is joint work with Jeffrey Bergfalk and Martino Lupini.
TUESDAY, February 16, 2021
Set Theory Reading Group: 4:30 P.M., Online, Aristotelis Panagiotopoulos,
University of Muenster
Join Zoom Meeting: https://cmu.zoom.us/j/621951121 [cmu.zoom.us]
Meeting ID: 621 951 121
TITLE: Ulam stability for quotients of abelian non-archimedean Polish groups
ABSTRACT: Based on an earlier work of Shelah concerning the relationship of the
continuum hypothesis to the cardinality of the set of automorphisms of
$\mathcal{P}(\omega)/\mathrm{fin}$, Velickovic showed that if such an
automorphism admits a Borel lift $\mathcal{P}(\omega)\to \mathcal{P}(\omega)$,
then it is of a certain "trivial" form. Similarly, Kanovei and Reeken showed
that if $N,M$ are countable dense subgroups of $\mathbb{R}$, then every
homomorphism $\mathbb{R}/N\to \mathbb{R}/M$ with a Borel lift $\mathbb{R}\to
\mathbb{R}$, is of a certain "trivial" form. Kanovei and Reeken asked whether
quotients of the $p$-adic groups satisfy similar "Ulam stability" phenomena. In
this talk, we will settle this question by providing Ulam-stability phenomena
for definable homomorphisms $G/N\to H/M$ when $G,H$ are arbitrary abelian
non-archimedean Polish groups and $N,M$ are Polishable subgroups. We will then
illustrate how such rigidity results are in the heart of the definable
cohomology theory which we developed in the previous talk.
This is joint work with Jeffrey Bergfalk and Martino Lupini.
On Logic Seminar This Semester
NUS Logic Seminar
1/19/2021 2:58:41
Dear Attendees of the logic seminar,
I would like to ask for volunteers who can give talks over Zoom at
17:00 hrs Singapore time, see
http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
for free time-slots (currently all and I will put the names of those
who reserve a slot into their preferred time-slot). Furthermore, for
tomorrow, you might consider attending the talk of Brian Rabern from
the University of Edinburgh at FASS on quantification as modelled by
Frege and by Taski and the philosophical discussion will be moderated
by Ben Blumson, NUS.
Best regards, Frank
`
(KGRC) research seminar talk on Thursday, January 21
Kurt Godel Research Center
1/18/2021 16:20:59
Research seminar
Kurt Gödel Research Center
Thursday, January 21
"Strong colourings over partitions"
Juris Steprāns
(York University, Toronto, Canada)
The celebrated result of Todorcevic that $\aleph_1\not\rightarrow
[\aleph_1]^2_{\aleph_1}$ provides a well known example of a strong colouring. A
mapping $c:[\omega_1]^2\to \kappa$ is a strong colouring over a partition
$p:[\omega_1]^2\to \omega$ if for every uncountable $X\subseteq \omega_1$ there
is $n\in \omega$ such that the range of $c$ on $[X]^2\cap p^{-1}\{n\}$ is all
of $\kappa$. I will discuss some recent work with A. Rinot and M. Kojman on
negative results concerning strong colourings over partitions and their
relation to classical results in this area.
Time and Place
Talk at 3:00pm via Zoom: This talk will be given via Zoom. If you have not
received the meeting link by the day before the talk, please contact
richard.springer@univie.ac.at!
Barcelona Set theory Seminar
Barcelona Logic Seminar
1/17/2021 15:37:58
Dear All,
Please find attached the announcement of the next session of the Barcelona Set Theory Seminar. Feel free to distribute it.
SPEAKER: Vera Fisher (Wien)
TITLE: Independent families in the countable and the uncountable
TIME: January 20 at 16:00 (CET)
PLACE: The Seminar will take place online at the following address:
Best regards,
Joan
P.S.: If you do not wish to receive any more announcements, please send an email to
bagaria@ub.edu with the text “Unsubscribe”.
Joan Bagaria
ICREA Research Professor
Universitat de Barcelona
Departament de Matemàtiques i Informàtica
Gran Via de les Corts Catalanes 585
08007 Barcelona
Catalonia
Phone: +34 93 402 1609
BLAST 2021: June 9-13
Conference
1/16/2021
BLAST 2021
June 9-13, 2021
New Mexico State University, Las Cruces, NM, USA
ONLINE
Conference website: https://math.nmsu.edu/blast-2021/
Conference email: blast@nmsu.edu
Submission link: https://easychair.org/conferences/?conf=blast2021
SCOPE
BLAST is a conference series focusing on Boolean Algebras, Lattices, Algebraic Logic, Universal Algebra, Set Theory, Set-theoretic Topology, and Point-free Topology. The series circulates between different universities. The central BLAST web page, with links to past meetings, can be found here: http://math.colorado.edu/blast/
This year's installment of BLAST will take place at New Mexico State University. The scientific program will include invited lectures, tutorial lectures, two special sessions, and contributed talks. Due to the current pandemic, the conference will be entirely online.
INVITED SPEAKERS:
Aichinger, Erhard (Johannes Kepler University Linz)
Carai, Luca (New Mexico State University)
Celani, Sergio (National University of the Center of the Buenos Aires Province)
Fisher, Vera (University of Vienna)
Gehrke, Mai (University of Cote d’Azur, Nice)
Hrusak, Michael (National Autonomous University of Mexico)
Lapenta, Serafina (University of Salerno)
Zamojska-Dzienio, Anna (Warsaw University of Technology)
TUTORIALS:
Bodirsky, Manuel (Dresden University of Technology)
Dow, Alan (UNC Charlotte)
Jung, Achim (University of Birmingham)
SPECIAL SESSIONS:
SPECIAL SESSION IN MEMORY OF W. CHARLES HOLLAND (1935—2020) AND JORGE MARTINEZ (1945—2020)
Organizers: Rick Ball (University of Denver) and Warren McGovern (Florida Atlantic University)
Speakers:
Ball, Rick (University of Denver)
Darnel, Michael (Indiana University South Bend)
Droste, Manfred (University of Leipzig)
Dube, Themba (University of South Africa)
Dvurečenskij, Anatolij (Mathematical Institute, Slovak Academy of Sciences)
Hager, Anthony (Wesleyan University)
Marra, Vincenzo (University of Milan)
McGovern, Warren (Florida Atlantic University)
Schwartz, Niels (University of Passau)
Tsinakis, Constantine (Vanderbilt University)
SPECIAL SESSION ON STONE AND PRIESTLEY DUALITIES
Speakers:
Borlido, Célia (University of Coimbra)
van Gool, Sam (University of Paris)
Holliday, Wesley (UC Berkeley)
Jibladze, Mamuka (Razmadze Mathematical Institute, Tbilisi State University)
Melliès, Paul-André (University of Paris)
Reggio, Luca (University of Oxford)
Salvati, Sylvain (University of Lille)
Tressl, Marcus (University of Manchester)
CONTRIBUTED TALKS:
Abstracts of contributed talks should be submitted through EasyChair:
https://easychair.org/conferences/?conf=blast2021
Please indicate if you would like to submit to a special session. The abstract should not exceed 2 pages.
IMPORTANT DATES:
11 April, 2021: Deadline for submitting abstracts of contributed talks
25 April, 2021: Notification of acceptance
9 June, 2021: Start of the conference
13 June, 2021: End of the conference
LOCAL ORGANIZING COMMITTEE:
Albee, Kempton (grad student)
Bezhanishvili, Guram
Carai, Luca (grad student)
Harding, John
Morandi, Pat
Olberding, Bruce
Peinado, Miguel (grad student)
Raviprakash, Ranjitha (grad student)
Shapirovsky, Ilya
Sinclaire, Morgan (grad student)
Tagged: Erhard Aichinger, Luca Carai, Sergio Celani, Vera Fisher, Mai Gehrke, Michael Hrusak, Serafina Lapenta, Anna Zamojska-Dzienio, Manuel Bodirsky, Alan Dow, Achim Jung, Rick Ball, Michael Darnel, Manfred Droste, Themba Dube, Anatolij Dvurečenskij, Anthony Hager, Vincenzo Marra, Warren McGovern, Niels Schwartz, Constantine Tsinakis, Célia Borlido, Sam van Gool, Wesley Holliday, Mamuka Jibladze, Paul-André Melliès, Luca Reggio, Sylvain Salvati, Marcus Tressl
Two events on February 2
Carnegie Mellon Logic Seminar
1/16/2021 10:43:13
TUESDAY, February 2, 2021
Mathematical logic seminar: 3:30 P.M., Online, Anush Tserunyan, McGill
University
Join Zoom Meeting: https://cmu.zoom.us/j/621951121 [cmu.zoom.us]
Meeting ID: 621 951 121
TITLE: Ergodic theorems along trees
ABSTRACT: In the classical pointwise ergodic theorem for a probability measure
preserving (pmp) transformation $T$, one takes averages of a given integrable
function over the intervals $\{x, T(x), T^2(x), \hdots, T^n(x)\}$ in front of
the point $x$. We prove a “backward” ergodic theorem for a countable-to-one pmp
$T$, where the averages are taken over subtrees of the graph of T that are
rooted at $x$ and lie behind $x$ (in the direction of $T^{-1}$). Surprisingly,
this theorem yields forward ergodic theorems for countable groups, in
particular, one for pmp actions of free groups of finite rank, where the
averages are taken along subtrees of the standard Cayley graph rooted at the
identity. This strengthens Bufetov’s theorem from 2000, which was the most
general result in this vein. This is joint work with Jenna Zomback.
TUESDAY, February 2, 2021
Set Theory Reading Group: 4:30 P.M., Online, Jenna Zomback, University of
Illinois at Urbana-Champaign
Join Zoom Meeting: https://cmu.zoom.us/j/621951121 [cmu.zoom.us]
Meeting ID: 621 951 121
TITLE: Ergodic theorems along trees: the proofs
ABSTRACT: In this continuation of the previous talk, we discuss a backward
(inverse) ergodic theorem for a probability measure preserving (pmp)
transformation $T$, where the averages are taken over subtrees of the graph of
$T$ that are rooted at $x$ and lie behind $x$ (in the direction of $T^{-1}$).
We will derive from it a new (forward) pointwise ergodic theorem for pmp
actions of free groups of finite rank, where the averages are taken along
subtrees of the standard Cayley graph rooted at the identity. We will then
discuss a very short proof (due to Tserunyan) of the classical pointwise
ergodic theorem, and, using this proof as an outline, we will sketch the proof
of the backward ergodic theorem. This is joint work with Anush Tserunyan.
Two talks next week (January 22nd)
Toronto Set Theory Seminar
1/15/2021 18:29:14
There was a Typo in the last email. Here the correction:
Speaker:Dima Sinapova, UIC, University of Illinois at Chicago, University of Illinois, Chicago
Date and Time: Friday, January 22, 2021 - 11am to 12:30pm
Abstract: (In previous email)
Speaker: Marcos Mazari Armida, Carnagie Mellon University
Date and Time: Friday, January 22, 2021 - 1:30pm to 3pm
Title: Universal models in classes of abelian groups and modules
Abstract: (In previous email)
Iván Ongay Valverde (he/his)
Hello everyone,
To start the semester we will have two talks: one at 11 am (Toronto time) and another at 1 30 pm (Toronto time).
Please use the following link and fill the form (every week) to
enter the meeting. This form helps the Field Institute to know
statistical data about attendance.
Here the speakers information:
Speaker:Dima Sinapova, UIC, University of Illinois at Chicago, University of Illinois, Chicago
Date and Time: Friday, January 22, 2021 - 11am to 12:30pm
Abstract:
Two classical results of Magidor are: (1) from large cardinals it is consistent to have reflection at
$\aleph_{\omega+1}$ and (2) from large cardinals it is consistent to have the failure of SCH at $\aleph_{\omega}$.
These principles are at odds with each other. The former is a
compactness type principle. (Compactness is the phenomenon where if a
certain property holds for every smaller substructure of an object, then
it holds for the entire object.) In contrast, failure of SCH is an
instance of incompactness. The natural question is whether we can have
both of these simultaneously. We show the answer is yes.
We describe a Prikry style iteration, and use it to force stationary
reflection in the presence of not SCH. Then we obtain this situation at
$\aleph_{\omega}$
. This is joint work with Alejandro Poveda and Assaf Rinot.
Speaker: Marcos Mazari Armida, Carnagie Mellon University
Date and Time: Friday, January 22, 2021 - 11am to 12:30pm
Title: Universal models in classes of abelian groups and modules
Abstract:
The search for universal models began in the early twentieth century when Hausdorff showed that there is a universal linear order of
cardinality $\aleph_{n+1}$ if $2^{\aleph_n}= \aleph_{n + 1}$, i.e., a
linear order $U$ of cardinality $\aleph_{n+1}$ such that every linear order of cardinality $\aleph_{n+1}$ embeds in $U$. In this talk, we will
study universal models in several classes of abelian groups and modules
with respect to pure embeddings. In particular, we will present a
complete solution below $\aleph_\omega$, with the exception of
$\aleph_0$ and $\aleph_1$, to Problem 5.1 in page 181 of \emph{Abelian
Groups} by L\'{a}szl\'{o} Fuchs, which asks to find the cardinals
$\lambda$ such that there is a universal abelian p-group for purity of
cardinality $\lambda$. The solution presented will use both
model-theoretic and set-theoretic ideas.
Iván Ongay Valverde (he/his)
Two talks next week (January 22nd)
Toronto Set Theory Seminar
1/15/2021 18:19:40
Hello everyone,
To start the semester we will have two talks: one at 11 am (Toronto time) and another at 1 30 pm (Toronto time).
Please use the following link and fill the form (every week) to
enter the meeting. This form helps the Field Institute to know
statistical data about attendance.
Here the speakers information:
Speaker:Dima Sinapova, UIC, University of Illinois at Chicago, University of Illinois, Chicago
Date and Time: Friday, January 22, 2021 - 11am to 12:30pm
Abstract:
Two classical results of Magidor are: (1) from large cardinals it is consistent to have reflection at
$\aleph_{\omega+1}$ and (2) from large cardinals it is consistent to have the failure of SCH at $\aleph_{\omega}$.
These principles are at odds with each other. The former is a
compactness type principle. (Compactness is the phenomenon where if a
certain property holds for every smaller substructure of an object, then
it holds for the entire object.) In contrast, failure of SCH is an
instance of incompactness. The natural question is whether we can have
both of these simultaneously. We show the answer is yes.
We describe a Prikry style iteration, and use it to force stationary
reflection in the presence of not SCH. Then we obtain this situation at
$\aleph_{\omega}$
. This is joint work with Alejandro Poveda and Assaf Rinot.
Speaker: Marcos Mazari Armida, Carnagie Mellon University
Date and Time: Friday, January 22, 2021 - 11am to 12:30pm
Title: Universal models in classes of abelian groups and modules
Abstract:
The search for universal models began in the early twentieth century when Hausdorff showed that there is a universal linear order of
cardinality $\aleph_{n+1}$ if $2^{\aleph_n}= \aleph_{n + 1}$, i.e., a
linear order $U$ of cardinality $\aleph_{n+1}$ such that every linear order of cardinality $\aleph_{n+1}$ embeds in $U$. In this talk, we will
study universal models in several classes of abelian groups and modules
with respect to pure embeddings. In particular, we will present a
complete solution below $\aleph_\omega$, with the exception of
$\aleph_0$ and $\aleph_1$, to Problem 5.1 in page 181 of \emph{Abelian
Groups} by L\'{a}szl\'{o} Fuchs, which asks to find the cardinals
$\lambda$ such that there is a universal abelian p-group for purity of
cardinality $\lambda$. The solution presented will use both
model-theoretic and set-theoretic ideas.
Iván Ongay Valverde (he/his)
(KGRC) research seminar talk on Thursday, January 14
Kurt Godel Research Center
1/11/2021 11:46:24
Research seminar
Kurt Gödel Research Center
Thursday, January 14
"Infinitary combinatorics and strong homology"
Jeffrey Bergfalk (KGRC)
Motivated by several recent advances, we will provide a research history
of the main set-theoretic problems arising in the study of strong
homology. As such, this talk will overlap with one on the same theme given
in Paris-Lyon Logic Seminar last fall. We will presume no awareness in our
audience either of strong homology or of that talk, but will aim in this
one to provide, along with the necessary background, some sketch of the
main ideas behind several recent arguments. This is an area in which
simplicial principles and infinitary combinatorics come together. Its
questions, at heart, have tended to be questions about higher-dimensional
variants of classical set-theoretic concerns (like nontrivial coherence,
$\Delta$ systems, etc.); these questions, in turn, increasingly appear to
be of some interest in their own right.
Time and Place
Talk at 3:00pm via Zoom: This talk will be given via Zoom. If you have not
received the meeting link by the day before the talk, please contact
richard.springer@univie.ac.at!
Barcelona Set theory Seminar
Barcelona Logic Seminar
1/11/2021 2:50:42
Dear All,
Please find attached the announcement of the next session of the Barcelona Set Theory Seminar. Feel free to distribute it.
SPEAKER: Trevor M. Wilson (Miami Univ.)
TITLE: The large cardinal strength of Vopenka's Principle for trees and for
rayless trees
TIME: January 13 at 16:00 (CET)
PLACE: The Seminar will take place online at the following address:
Best regards,
Joan
P.S.: If you do not wish to receive any more announcements, please send an email to
bagaria@ub.edu with the text “Unsubscribe”.
Joan Bagaria
ICREA Research Professor
Universitat de Barcelona
Departament de Matemàtiques i Informàtica
Gran Via de les Corts Catalanes 585
08007 Barcelona
Catalonia
Phone: +34 93 402 1609
Logic Seminar at NUS on Wednesday 13 Jan 2021 17:00 hrs - World Logic Day Special
NUS Logic Seminar
1/10/2021 23:33:48
Dear colleagues,
This week's Logic Seminar on Wed 13 January 2021 at 17:00 hrs is an
open session where, in light of the World Logic Day on Thursday, everyone
is encouraged to give a 5 to 10 minutes presentation about his favourate
result or results of his own work. In the case that you have no slides
for this, feel free to share a Word file and type into it on Zoom.
The result can be from any time where you have been working on logic,
it should give the statement and contribution of the theorem. If you
want to give a longer talk, we will schedule one in the next weeks.
Best regards, Frank
Here again the details:
Wednesday 13 Jan 2021 17:00 hrs Singapore Time (+800)
World Logic Seminar Special - Share your nicest results
Discussion via Zoom:
https://nus-sg.zoom.us/j/96860201432?pwd=cVdwZmd2clVFaEhaTmJjaGdXMFdmdz09
Meeting ID: 968 6020 1432
Password: Is P=NP?
You might reply with a short email to Frank Stephan (fstephan@comp.nus.edu.sg)
and Yang Yue (matyangy@nus.edu.sg) if you follow our request for a short talk
of 5 to 10 minutes, just for planning purposes.
Best regards, Frank
(KGRC) research seminar talk on Thursday, December 17
Kurt Godel Research Center
12/14/2020 10:27:53
Research seminar
Kurt Gödel Research Center
Thursday, December 17
"Ramsey-like Operators"
Peter Holy (University of Udine, Italy)
Starting from measurability upwards, larger large cardinals are usually
characterized by the existence of certain elementary embeddings of the
universe, or dually, the existence of certain ultrafilters. However, below
measurability, we have a somewhat similar picture when we consider certain
embeddings with set-sized domain, or ultrafilters for small collections of
sets. I will present some new results, and also review some older ones, showing
that not only large cardinals below measurability, but also several related
concepts can be characterized in such a way, and I will also provide a sample
application of these characterizations.
Time and Place
Talk at 3:00pm via Zoom: This talk will be given via Zoom. If you have not
received the meeting link by the day before the talk, please contact
richard.springer@univie.ac.at!
Barcelona Set Theory Seminar
Barcelona Logic Seminar
12/14/2020 2:36:18
Dear All,
Please find attached the announcement of the next session of the Barcelona Set Theory Seminar. Feel free to distribute it.
SPEAKER: Victoria Gitman (CUNY)
TITLE: Characterizing large cardinals via abstract logics
TIME: December 16 at 16:00 (CET)
PLACE: The Seminar will take place online at the following address:
Best regards,
Joan
P.S.: If you do not wish to receive any more announcements, please send an email to
bagaria@ub.edu with the text “Unsubscribe”.
Joan Bagaria
ICREA Research Professor
Universitat de Barcelona
Departament de Matemàtiques i Informàtica
Gran Via de les Corts Catalanes 585
08007 Barcelona
Catalonia
Phone: +34 93 402 1609
This Week in Logic at CUNY
This Week in Logic at CUNY
12/13/2020 19:59:02
Hi everyone,
The coming week is final exams at CUNY, which will be followed by our winter break. This will be the last edition of "This Week in Logic" until the New Year. Have a happy holiday season!
Best,
Jonas
This Week in Logic at CUNY:
- - - - Monday, Dec 14, 2020 - - - -
Logic and Metaphysics Workshop
ST and All That: Philosophical Issues
This will be a round table. Speakers (15 minutes each), followed by an open discussion:
Shay Logan (Kansas State)
Federico Pailos (Buenos Aires)
Dave Ripley (Monash)
Chris Scambler (NYU)
We may go on somewhat longer than the usual two hours if the discussion is productive. The meeting is open to all interested.
- - - - Tuesday, Dec 15, 2020 - - - -- - - - Wednesday, Dec 16, 2020 - - - -The New York City Category Theory Seminar
Speaker: Arthur Parzygnat, IHES.
Date and Time: Wednesday December 16, 2020, 1:00 - 2:30 PM. ***NOTICE THE SPECIAL TIME***, on Zoom.
Title: A functorial characterization of classical and quantum entropies.
Abstract: Entropy appears as a useful concept in a wide variety of academic disciplines. As such, one would suspect that category theory would provide a suitable language to encompass all or most of these definitions. The Shannon entropy has recently been given a characterization as a certain affine functor by Baez, Fritz, and Leinster. This characterization is the only characterization I know of that uses linear assumptions (as opposed to additive, exponential, logarithmic, etc). Here, we extend that characterization to include the von Neumann entropy as well as highlight the new categorical structures that arise when trying to do so. In particular, we introduce Grothendieck fibrations of convex categories, and we review the notion of a disintegration, which is a key part of conditional probability and Bayesian statistics and plays a crucial role in our characterization theorem. The characterization of Baez, Fritz, and Leinster interprets Shannon entropy in terms of the information loss associated to a deterministic process, which is possible since the entropy difference associated to such a process is always non-negative. This fails for quantum entropy, and has important physical consequences.
References:
Paper (and references therein)
Paper (original paper of Baez, Fritz, and Leinster)
- - - - Thursday, Dec 17, 2020 - - - -Philog Seminar
Thursday, December 17, 6:30 PM EST
Barbara H. Partee, Department of Linguistics, University of Massachusetts Amherst
Language and Logic: Ideas and Controversies in the History of Formal Semantics
(As a very senior and accomplished linguist she is the right person to tell us about formal semantics.)
Brief abstract: The history of formal semantics and pragmatics over the last 50 years is a story of collaboration among linguists, logicians, and philosophers. Since this talk is for a seminar in philosophy, logic, and games, and I’m a linguist, I’ll emphasize aspects of the pre-history and history of formal semantics that concern the relation between language and logic, not presupposing knowledge of linguistics.
Zoom link will be posted on
https://philog.arthurpaulpedersen.org/
- - - - Friday, Dec 18, 2020 - - - -
Next Week in Logic at CUNY:
- - - - Monday, Dec 21, 2020 - - - -
- - - - Tuesday, Dec 22, 2020 - - - -
- - - - Wednesday, Dec 23, 2020 - - - -
- - - - Thursday, Dec 24, 2020 - - - -
- - - - Friday, Dec 25, 2020 - - - -
- - - - Other Logic News - - - -
- - - - Web Site - - - -
Find us on the web at:
nylogic.github.io(site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to
jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email
jreitz@nylogic.org.
(KGRC) research seminar talk on Thursday, December 10
Kurt Godel Research Center
12/7/2020 10:26:42
Research seminar
Kurt Gödel Research Center
Thursday, December 10
"Invariant Ideal Axiom"
Michael Hrušák (UNAM, Mexico City, Mexico)
We shall introduce a consistent set-theoretic axiom which has a profound impact
on convergence properties in topological groups. As an application we show that
consistently (consequence of IIA) every countable sequential group is either
metrizable or $k_\omega$.
Time and Place
Talk at 3:00pm via Zoom: This talk will be given via Zoom. If you have not
received the meeting link by the day before the talk, please contact
richard.springer@univie.ac.at!
This Week in Logic at CUNY
This Week in Logic at CUNY
12/6/2020 22:22:28
This Week in Logic at CUNY:
- - - - Monday, Dec 7, 2020 - - - -
Logic and Metaphysics Workshop
Date: Monday, December 7, 4.15-6.15 (NY time)
For meeting information, please email: yweiss@gradcenter.cuny.edu
Jennifer McDonald (CUNY)
Title: Essential Structure and Apt Causal Models
Abstract: A promising account of actual causation – the causal relation holding between two token events – uses the language of structural equation models (SEMs). Such an account says, roughly, that actual causation holds between two token events when there is a suitable model according to which (1) the two events occur; and (2) intervening on the model to change the value of the variable that represents the cause changes the value of the variable that represents the effect (Halpern & Pearl, 2005; Hitchcock, 2001; Weslake, 2015; Woodward, 2003). Of course, this calls for an account of when a model is suitable – or, apt. Although initially bracketed, this issue is increasingly pressing; in part due to the recently discovered problem of structural isomorphs (Hall 2007; Hitchcock 2007a; Blanchard and Schaffer 2017; Menzies 2017). This paper offers a unified analysis of two aptness requirements from the literature – those enjoining us to include essential structure and avoid unstable models. While successfully invoked by Blanchard and Schaffer (2017) to resolve the problem of structural isomorphs, these requirements are unilluminating as they stand. My paper synthesizes them into a single aptness requirement that, I claim, gets to the heart of what’s representationally required of a causal model for capturing actual causation.
- - - - Tuesday, Dec 8, 2020 - - - -
- - - - Wednesday, Dec 9, 2020 - - - -
Models of Peano Arithmetic (MOPA)
The seminar will take place virtually at 3pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.Wednesday, Dec 9, 3pm
Konrad Zdanowski, Cardinal Stefan Wyszynski University in Warsaw
Truth predicate for Δ0Δ0 formulas and PSPACE computations
We consider a bounded arithmetic in Buss's language enriched with a predicate Tr which is assumed to be a truth definition for bounded sentences. Among other things we assume polynomial induction for Σb1(Tr)Σ1b(Tr) formulas. We show that such an arithmetic captures PSPACE. We prove a witnessing theorem for such an arithmetic by an interpretation of free-cuts free proofs of strict Σ1,b1Σ11,b in U1,∗2U21,∗, a canonical second order arithmetic capturing PSPACE. It follows that the problem of the existence of a truth definition for Δ0Δ0 sentences without the totality of expexp might be more about separating subexponential time alternation hierarchies from PSPACE.
The presentation is based on the following article: Konrad Zdanowski, Truth definition for Δ0Δ0 formulas and PSPACE computations, Fundamenta Mathematicae 252(2021) , 1-38.
The New York City Category Theory Seminar
Speaker: Dan Shiebler, Oxford University.
Date and Time: Wednesday December 9, 2020, 7:00 - 8:30 PM., on Zoom.
Title: Functorial Manifold Learning and Overlapping Clustering.
Abstract: We adapt previous research on functorial clustering and topological unsupervised learning to develop a functorial perspective on manifold learning algorithms. Our framework characterizes a manifold learning algorithm in terms of the loss function that it optimizes, which allows us to focus on the algorithm's objective rather than the details of the learning process. We demonstrate that we can express several state of the art manifold learning algorithms, including Laplacian Eigenmaps, Metric Multidimensional Scaling, and UMAP, as functors in this framework. This functorial perspective allows us to reason about the invariances that these algorithms preserve and prove refinement bounds on the kinds of loss functions that any such functor can produce. Finally, we experimentally demonstrate how this perspective enables us to derive and analyze novel manifold learning algorithms.
- - - - Thursday, Dec 10, 2020 - - - -
- - - - Friday, Dec 11, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, Dec 11, 11am
The seminar will take place virtually at 11am US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. Dima Sinapova, University of Chicago
Iteration, reflection, and singular cardinals
There is an inherent tension between stationary reflection and the failure of the singular cardinal hypothesis (SCH). The former is a compactness type principle that follows from large cardinals. Compactness is the phenomenon where if a certain property holds for every smaller substructure of an object, then it holds for the entire object. In contrast, failure of SCH is an instance of incompactness.
Two classical results of Magidor are:
(1) from large cardinals it is consistent to have reflection at ℵω+1ℵω+1, and
(2) from large cardinals it is consistent to have the failure of SCH at ℵωℵω.
As these principles are at odds with each other, the natural question is whether we can have both. We show the answer is yes.
We describe a Prikry style iteration, and use it to force stationary reflection in the presence of not SCH. Then we obtain this situation at ℵωℵω by interleaving collapses. This is joint work with Alejandro Poveda and Assaf Rinot.
Next Week in Logic at CUNY:
- - - - Monday, Dec 14, 2020 - - - -
- - - - Tuesday, Dec 15, 2020 - - - -- - - - Wednesday, Dec 16, 2020 - - - -The New York City Category Theory Seminar
Speaker: Arthur Parzygnat, IHES.
Date and Time: Wednesday December 16, 2020, 1:00 - 2:30 PM. ***NOTICE THE SPECIAL TIME***, on Zoom.
Title: A functorial characterization of classical and quantum entropies.
Abstract: Entropy appears as a useful concept in a wide variety of academic disciplines. As such, one would suspect that category theory would provide a suitable language to encompass all or most of these definitions. The Shannon entropy has recently been given a characterization as a certain affine functor by Baez, Fritz, and Leinster. This characterization is the only characterization I know of that uses linear assumptions (as opposed to additive, exponential, logarithmic, etc). Here, we extend that characterization to include the von Neumann entropy as well as highlight the new categorical structures that arise when trying to do so. In particular, we introduce Grothendieck fibrations of convex categories, and we review the notion of a disintegration, which is a key part of conditional probability and Bayesian statistics and plays a crucial role in our characterization theorem. The characterization of Baez, Fritz, and Leinster interprets Shannon entropy in terms of the information loss associated to a deterministic process, which is possible since the entropy difference associated to such a process is always non-negative. This fails for quantum entropy, and has important physical consequences.
References:
Paper (and references therein)
Paper (original paper of Baez, Fritz, and Leinster)
- - - - Thursday, Dec 17, 2020 - - - -- - - - Friday, Dec 18, 2020 - - - -
- - - - Other Logic News - - - -
- - - - Web Site - - - -
Find us on the web at:
nylogic.github.io(site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to
jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email
jreitz@nylogic.org.
Barcelona Set Theory Seminar
Barcelona Logic Seminar
12/4/2020 6:51:20
Dear All,
Please find attached the announcement of the next session of the Barcelona Set Theory Seminar. Feel free to distribute it.
SPEAKER: Neil Barton (University of Konstanz)
TITLE: Intensional classes and intuitionistic topoi
TIME: December 9 at 16:00 (CET)
PLACE: The Seminar will take place online at the following address:
Best regards,
Joan
P.S.: If you do not wish to receive any more announcements, please send an email to
bagaria@ub.edu with the text “Unsubscribe”.
Joan Bagaria
ICREA Research Professor
Universitat de Barcelona
Departament de Matemàtiques i Informàtica
Gran Via de les Corts Catalanes 585
08007 Barcelona
Catalonia
Phone: +34 93 402 1609
Set theory in the UK workshop, online, December 4
Conference
12/1/2020
The next Set Theory in the UK workshop will take place online on Friday, 4 December 2020, from 9.30am-2pm.
Please see the meeting's website http://www1.maths.leeds.ac.uk/~pmtadb/STUK6/STUK6.html for more information.
How to participate: Information how to obtain a login will be available on the conference website soon. Please find this information in advance, on the day before the meeting.
09.30-09.55 Yair Hayut (Hebrew University of Jerusalem): Generics via ultrapowers
10.00-10.50 Arno Pauly (Swansea University): Luzin's (N) and randomness reflection
11.00-11.50 Peter Holy (University of Udine): Ramsey-like operators
lunch break
13.30-13.55 Jiachen Yuan (University of East Anglia): Indestructibility of supercompactness and large cardinals
Titles and abstracts:
Yair Hayut: Generics via ultrapowers
Bukovský and Dehornoy observed (independently) that there is a generic for the Prikry forcing over the iterated ultrapower by the measure. I will show how one can use this fact in order to derive (without referring to the forcing) many interesting properties of the generic extension.
Arno Pauly: Luzin's (N) and randomness reflection
Peter Holy: Ramsey-like operators
Starting from measurability upwards, larger large cardinals are usually characterized by the existence of certain elementary embeddings of the universe, or dually, the existence of certain ultrafilters. However, below measurability, we have a somewhat similar picture when we consider certain embeddings with set-sized domain, or ultrafilters for small collections of sets. I will present some new results, and also review some older ones, showing that not only large cardinals below measurability, but also several related concepts can be characterized in such a way, and I will also provide a sample application of these characterizations.
Jiachen Yuan: Indestructibility of supercompactness and large cardinals
It is well known that "there is a supercompact cardinal which is immune to any $\kappa-$directed closed set forcing" is relatively consistent with "there is a supercompact cardinal". We also know that there is no analogue of such a theorem to any large cardinal stronger than extendible. In fact, provably in $ZFC$ such large cardinal properties will be destroyed by any $\kappa-$directed closed set forcing. For larger cardinals, according to a theorem of Usuba, they can not survive in any set-forcing extension which is not equivalent to a small forcing. However, it was not known if it is possible to have such a large cardinal notion with its supercompactness indestructible. It turns out that this is true for a lot of large cardinals by forcing from a ground model with the same strength.
See you at the meeting!
Andrew Brooke-Taylor, Asaf Karagila and Philipp Schlicht
Tagged: Yair Hayut, Arno Pauly, Peter Holy, Jiachen Yuan
Talk this Friday 2 hours-long (1 30 pm Toronto time)
Toronto Set Theory Seminar
11/30/2020 13:27:39
Hello all,
This week:
Date: Friday December 4, 1.30pm (2 hours long)
location: Online
Please use the following link and fill the form (every week) to enter
the meeting. This form helps the Field Institute to know statistical
data about attendance.
https://zoom.us/meeting/register/tJUvcO2tqTMqEtdESHljnD_Ee4rneqRCkDqo
Speaker: Thomas Daniells Gilton
Affiliation: Department of Mathematics, The University of Pittsburgh
Title: The Abraham-Rubin-Shelah Open Coloring Axiom with a Large
Continuum
Abstract:
Open Coloring Axioms may be viewed as consistent generalizations of
Ramsey's Theorem to $\omega_1$ in which topological restrictions are
placed on the colorings. The first of these, denoted
$\mathsf{OCA}_{ARS}$, appeared in the 1985 paper by Abraham, Rubin, and
Shelah. There the authors showed that $\mathsf{OCA}_{ARS}$ is consistent
with $\mathsf{ZFC}$. To ensure that the posets which add the homogeneous
sets satisfy the c.c.c., they construct a type of ``diagonalization"
object (for a continuous coloring $\chi$) called a \emph{Preassignment
of Colors}, which guides the forcing to add the $\chi$-homogeneous sets.
However, the only known constructions of effective preassignments
require the $\mathsf{CH}$. Since a forcing iteration of $\aleph_1$-sized
posets all of whose proper initial segments satisfy the $\mathsf{CH}$
results in a model in which $2^{\aleph_0}$ is at most $\aleph_2$, this
leads naturally to the question of whether $\mathsf{OCA}_{ARS}$ is
consistent, say, with $2^{\aleph_0}=\aleph_3$.
In joint work with Itay Neeman, we answer this question in the
affirmative. In light of the $\mathsf{CH}$ obstacle, we only construct
names for preassignments with respect to a small class $\mathcal{A}$ of
$\mathsf{CH}$-preserving iterations. However, our preassignments are
powerful enough to work even over models in which the $\mathsf{CH}$
fails.
Our final forcing is built by combining the members of $\mathcal{A}$
into a new type of forcing, called a \emph{Partition Product}. A
partition product is a type of restricted memory iteration with
isomorphism and coherent-overlap conditions on the memories. In
particular, each ``memory" is isomorphic to a member of $\mathcal{A}$.
In this talk, we will describe in some detail the definition of a
Partition Product. We will then discuss how to construct more general
preassignments than those used by Abraham, Rubin, and Shelah, gesturing
at the end towards the full construction which we use for our theorem.
========================================
Speaker Bio:
I am a Visiting Assistant Professor in the department of Mathematics at
the University of Pittsburgh, having graduated from UCLA in the Fall of
2019 under the supervision of Itay Neeman. I am interested in questions
about what combinatorial principles determine the size of the continuum,
as well as in questions about the tension between compactness and
incompactness principles in set theory. I reside in Pittsburgh with my
wife, Marian (who is a philosopher of physics), with our indefatigable
toddler Zoe, and with our two cats.
See you then!
Iván Ongay Valverde (he/his)
(KGRC) research seminar talk on December 3
Kurt Godel Research Center
11/30/2020 10:32:23
Research seminar
Kurt Gödel Research Center
Thursday, December 3
"On logics that make a bridge from the Discrete to the Continuous"
Mirna Džamonja
(CNRS & Panthéon Sorbonne, Paris, France and Czech Academy of Sciences, Prague)
The talk starts with a surveys of some recent connections between logic
and discrete mathematics. Then we discuss logics which model the passage
between an infinite sequence of finite models to an uncountable limiting
object, such as is the case in the context of graphons. Of particular
interest is the connection between the countable and the uncountable
object that one obtains as the union versus the combinatorial limit of the
same sequence. We compare such logics and discuss some consequences of
such comparisons, as well as some hopes for further results in this
research project.
Time and Place
Talk at 3:00pm via Zoom: This talk will be given via Zoom. If you have not
received the meeting link by the day before the talk, please contact
richard.springer@univie.ac.at!
This Week in Logic at CUNY
This Week in Logic at CUNY
11/29/2020 21:56:09
This Week in Logic at CUNY:
- - - - Monday, Nov 23, 2020 - - - -
Logic and Metaphysics Workshop
Date: Monday, November 23, 4.15-6.15 (NY time)
For meeting information, please email: yweiss@gradcenter.cuny.edu Behnam Zolghadr (LMU Munich)
Title: How to Abū Hāšim Meinong
Abstract: Similar to Meinong, Abū Hāšim al-Ǧubbāī (d.933), an Islamic theologian/philosopher, held the view that some objects do not exist. This paper is a comparative study between Meinong’s object theory and Abū Hāšim’s theory of nonexistent objects. Our comparative study will be carried out through three main topics: the characterization principle, objecthood, and the ontological status of existence itself. Moreover, Abū Hāšim and his followers argue that the view that some objects do not exist implies some truth value gaps and/or gluts. We will also discuss two of these arguments.
- - - - Tuesday, Nov 24, 2020 - - - -
Computational Logic Seminar
Tuesday November 24, 2-4pm
Ask Sergei Artemov for the (usual) link, unless you already have it.
Speaker: Stepan Kuznetsov, Steklov Mathematical Institute, Russian Academy of Sciences
Title: Ad hoc algebraic models for non-standard Kleene stars
Abstract: Kleene iteration, or Kleene star, is one of the most intriguing algebraic operations appearing in theoretical computer science. In most conventional models, the Kleene star a* is interpreted as the union (limit) of n-th powers of a. In relational structures, this corresponds to reflexive-transitive closure, in language models it is iteration of languages, and so on. Such interpretation of the Kleene star is called *-continuous. However, the usual axiomatization of the Kleene star using induction principles (as opposed to the omega-rule), is essentially weaker and, thus, admits a broader class of models. Existence of nonstandard, non-*-continuous models can be easily proved non-constructively. However, in order to use such models for studying substructural logics with Kleene star one has to construct them explicitly. In this talk, we show two of such models, constructed for proving some facts about derivability in extensions of the Lambek calculus with the Kleene star. Both models are ad hoc algebraic constructions, and we do not yet know whether they could fit in a natural family of models.
The talk is based on my AiML 2018 and AiML 2020 papers
- - - - Wednesday, Nov 25, 2020 - - - -
- - - - Thursday, Nov 26, 2020 - - - -
THANKSGIVING RECESS
- - - - Friday, Nov 27, 2020 - - - -
THANKSGIVING RECESS
Next Week in Logic at CUNY:
- - - - Monday, Nov 30, 2020 - - - -
Logic and Metaphysics Workshop
Date: Monday, November 30, 4.15-6.15 (NY time)
For meeting information, please email: yweiss@gradcenter.cuny.edu Mircea Dumitru (Bucharest)
Title: A Free Logic for Fictionalism
Abstract: In Reference without Referents, Mark Sainsbury aims to provide an account of reference that honours the common-sense view that sentences containing empty names like “Sherlock Holmes”, “Vulcan”, and “Santa Claus” are entirely intelligible, and that many such sentences — “Vulcan doesn’t exist”, “Many children believe that Santa Claus will give them presents at Christmas”, etc.— are literally true. Sainsbury’s account endorses the Davidsonian program in the theory of meaning, and combines this with a commitment to Negative Free Logic, which holds that all simple sentences containing empty names are false. In my talk, I pose a number of problems for this account. In particular, I question the ability of Negative Free Logic to make appropriate sense of the truth of familiar sentences containing empty names, including negative existential claims like “Vulcan doesn’t exist”.
Note: this is based on joint work with Frederick Kroon (Auckland).
- - - - Tuesday, Dec 1, 2020 - - - -
Computational Logic Seminar
Tuesday December 1, 2-4pm
Ask Sergei Artemov for the (usual) link, unless you already have it.
Speaker: Rohit Parikh, Brooklyn College and CUNY Graduate Center
Title: TOPOLOGY AND EPISTEMIC LOGIC
Abstract. We present the main ideas behind a number of logical systems for reasoning about points and sets that incorporate knowledge-theoretic ideas, and also the main results about them. Some of our discussions will be about applications of modal ideas to topology, and some will be on applications of topological ideas in modal logic, especially in epistemic logic.
In the former area, we would like to present the basic ideas and results of topologic, the study of two-sorted bimodal logical systems interpreted on subset spaces; these are arbitrary sets with collections of subsets called opens. Many of the papers in this field deal with questions of axiomatizing the logics of particular classes of subset spaces determined by conditions on the “opens”, such as being closed under intersection, being topologies, or satisfying various chain conditions.
Work in this area has been done by RP as well as Larry Moss (Indiana), Andrew Dabrowski (Indiana), K Georgatos (CUNY), Angela Weiss (CUNY), Chris Steinsvold (CUNY), Bernhard Heinemann (Hagen), Can Baskent (CUNY) and many others.
- - - - Wednesday, Dec 2, 2020 - - - -
- - - - Thursday, Dec 3, 2020 - - - -
- - - - Friday, Dec 4, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, Dec 4, 3pm
The seminar will take place virtually at 3pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. Zach Norwood, University of Michigan
TBA
Next Week in Logic at CUNY:
- - - - Monday, Dec 7, 2020 - - - -
Logic and Metaphysics Workshop
Date: Monday, December 7, 4.15-6.15 (NY time)
For meeting information, please email: yweiss@gradcenter.cuny.edu
Jennifer McDonald (CUNY)
Title: Essential Structure and Apt Causal Models
Abstract: A promising account of actual causation – the causal relation holding between two token events – uses the language of structural equation models (SEMs). Such an account says, roughly, that actual causation holds between two token events when there is a suitable model according to which (1) the two events occur; and (2) intervening on the model to change the value of the variable that represents the cause changes the value of the variable that represents the effect (Halpern & Pearl, 2005; Hitchcock, 2001; Weslake, 2015; Woodward, 2003). Of course, this calls for an account of when a model is suitable – or, apt. Although initially bracketed, this issue is increasingly pressing; in part due to the recently discovered problem of structural isomorphs (Hall 2007; Hitchcock 2007a; Blanchard and Schaffer 2017; Menzies 2017). This paper offers a unified analysis of two aptness requirements from the literature – those enjoining us to include essential structure and avoid unstable models. While successfully invoked by Blanchard and Schaffer (2017) to resolve the problem of structural isomorphs, these requirements are unilluminating as they stand. My paper synthesizes them into a single aptness requirement that, I claim, gets to the heart of what’s representationally required of a causal model for capturing actual causation.
- - - - Tuesday, Dec 8, 2020 - - - -
- - - - Wednesday, Dec 9, 2020 - - - -
- - - - Thursday, Dec 10, 2020 - - - -
- - - - Friday, Dec 11, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, Dec 11, 11am
The seminar will take place virtually at 11am US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. Dima Sinapova, University of Chicago
TBA
- - - - Other Logic News - - - -
- - - - Web Site - - - -
Find us on the web at:
nylogic.github.io(site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to
jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email
jreitz@nylogic.org.
Barcelona Set Theory Seminar
Barcelona Logic Seminar
11/29/2020 5:10:28
Dear All,
Please find attached the announcement of the next session of the Barcelona Set Theory Seminar. Feel free to distribute it.
SPEAKER: Toby Meadows (UC Irvine)
TITLE: What set theory could not be
TIME: December 2 at 16:00 (CET)
PLACE: The Seminar will take place online at the following address:
Best regards,
Joan
P.S.: If you do not wish to receive any more announcements, please send an email to
bagaria@ub.edu with the text “Unsubscribe”.
Joan Bagaria
ICREA Research Professor
Universitat de Barcelona
Departament de Matemàtiques i Informàtica
Gran Via de les Corts Catalanes 585
08007 Barcelona
Catalonia
Phone: +34 93 402 1609
Reminder: Talk tomorrow at 1 30
Toronto Set Theory Seminar
11/26/2020 14:29:00
Please use the following link and fill the form (every week) to
enter the meeting. This form helps the Field Institute to know
statistical data about attendance.
Speaker: Sandra Müller, University of Vienna
Date and Time: Friday, November 27, 2020 - 1:30pm to 3:00pm
Abstract:
The study of inner models was initiated by Gödel’s analysis of the constructible universe L
.
Later, it became necessary to study canonical inner models with large
cardinals, e.g. measurable cardinals, strong cardinals or Woodin
cardinals, which were introduced by Jensen, Mitchell, Steel, and others.
Around the same time, the study of infinite two-player games was driven
forward by Martin’s proof of analytic determinacy from a measurable
cardinal, Borel determinacy from ZFC, and Martin and Steel’s proof of
levels of projective determinacy from Woodin cardinals with a measurable
cardinal on top. First Woodin and later Neeman improved the result in
the projective hierarchy by showing that in fact the existence of a
countable iterable model, a mouse, with Woodin cardinals and a top
measure suffices to prove determinacy in the projective hierarchy.
This opened up the possibility for an optimal result stating the
equivalence between local determinacy hypotheses and the existence of
mice in the projective hierarchy, just like the equivalence of analytic
determinacy and the existence of x♯
for every real x
which was shown by Martin and Harrington in the 70’s. The existence of
mice with Woodin cardinals and a top measure from levels of projective
determinacy was shown by Woodin in the 90’s. Together with his earlier
and Neeman’s results this estabilishes a tight connection between
descriptive set theory in the projective hierarchy and inner model
theory.
In this talk, we will outline some of the main results connecting
determinacy hypotheses with the existence of mice with large cardinals
and discuss a number of more recent results in this area.
On Friday Dec. 4th we will have Thomas Gilton. Please, also see the webpage http://www.fields.utoronto.ca/activities/20-21/set-theory-seminar
Iván Ongay Valverde (he/his)
Sandra Muller Talk this Friday 1 30 pm
Toronto Set Theory Seminar
11/23/2020 13:27:26
Please use the following link and fill the form (every week) to
enter the meeting. This form helps the Field Institute to know
statistical data about attendance.
Speaker: Sandra Müller, University of Vienna
Date and Time: Friday, November 27, 2020 - 1:30pm to 3:00pm
Abstract:
The study of inner models was initiated by Gödel’s analysis of the constructible universe L
.
Later, it became necessary to study canonical inner models with large
cardinals, e.g. measurable cardinals, strong cardinals or Woodin
cardinals, which were introduced by Jensen, Mitchell, Steel, and others.
Around the same time, the study of infinite two-player games was driven
forward by Martin’s proof of analytic determinacy from a measurable
cardinal, Borel determinacy from ZFC, and Martin and Steel’s proof of
levels of projective determinacy from Woodin cardinals with a measurable
cardinal on top. First Woodin and later Neeman improved the result in
the projective hierarchy by showing that in fact the existence of a
countable iterable model, a mouse, with Woodin cardinals and a top
measure suffices to prove determinacy in the projective hierarchy.
This opened up the possibility for an optimal result stating the
equivalence between local determinacy hypotheses and the existence of
mice in the projective hierarchy, just like the equivalence of analytic
determinacy and the existence of x♯
for every real x
which was shown by Martin and Harrington in the 70’s. The existence of
mice with Woodin cardinals and a top measure from levels of projective
determinacy was shown by Woodin in the 90’s. Together with his earlier
and Neeman’s results this estabilishes a tight connection between
descriptive set theory in the projective hierarchy and inner model
theory.
In this talk, we will outline some of the main results connecting
determinacy hypotheses with the existence of mice with large cardinals
and discuss a number of more recent results in this area.
On Friday Dec. 4th we will have Thomas Gilton. Please, also see the webpage http://www.fields.utoronto.ca/activities/20-21/set-theory-seminar
Iván Ongay Valverde (he/his)
(KGRC) research seminar talk on Thursday, November 26
Kurt Godel Research Center
11/23/2020 9:54:24
Research seminar
Kurt Gödel Research Center
Thursday, November 26
"Convergence of Borel measures and filters on omega"
Damian Sobota (KGRC)
The celebrated Josefson--Nissenzweig theorem asserts, under certain
interpretations, that for every infinite compact space K there exists a
sequence of normalized signed Borel measures on K which converges to 0 with
respect to every continuous real-valued function (i.e. the corresponding
integrals converge to 0). We showed that in the case of products of two
infinite compact spaces K and L one can construct such a sequence of measures
with an additional property that every measure has finite support---let us call
such a sequence ``an fsJN-sequence'' (i.e. a finitely supported
Josefson--Nissenzweig sequence). We then studied the case when the spaces K and
L are only pseudocompact and we proved in ZFC that if the product of K and L is
pseudocompact, then it also admits an fsJN-sequence. On the other hand, we
showed that under the Continuum Hypothesis, or Martin's axiom, or even some
weaker set-theoretic assumptions concerning weak P-points, there exists a
pseudocompact space X such that its square is not pseudocompact and it does not
admit any fsJN-sequences. During my talk I will discuss these as well as other
results concerning the topic and obtained during a joint work with various
combinations of J. Kakol, W. Marciszewski and L. Zdomskyy.
Time and Place
Talk at 3:00pm via Zoom: This talk will be given via Zoom. If you have not
received the meeting link by the day before the talk, please contact
richard.springer@univie.ac.at!
This Week in Logic at CUNY
This Week in Logic at CUNY
11/22/2020 20:32:48
This Week in Logic at CUNY:
- - - - Monday, Nov 23, 2020 - - - -
Logic and Metaphysics Workshop
Date: Monday, November 23, 4.15-6.15 (NY time)
For meeting information, please email: yweiss@gradcenter.cuny.edu Behnam Zolghadr (LMU Munich)
Title: How to Abū Hāšim Meinong
Abstract: Similar to Meinong, Abū Hāšim al-Ǧubbāī (d.933), an Islamic theologian/philosopher, held the view that some objects do not exist. This paper is a comparative study between Meinong’s object theory and Abū Hāšim’s theory of nonexistent objects. Our comparative study will be carried out through three main topics: the characterization principle, objecthood, and the ontological status of existence itself. Moreover, Abū Hāšim and his followers argue that the view that some objects do not exist implies some truth value gaps and/or gluts. We will also discuss two of these arguments.
- - - - Tuesday, Nov 24, 2020 - - - -
Computational Logic Seminar
Tuesday November 24, 2-4pm
Ask Sergei Artemov for the (usual) link, unless you already have it.
Speaker: Stepan Kuznetsov, Steklov Mathematical Institute, Russian Academy of Sciences
Title: Ad hoc algebraic models for non-standard Kleene stars
Abstract: Kleene iteration, or Kleene star, is one of the most intriguing algebraic operations appearing in theoretical computer science. In most conventional models, the Kleene star a* is interpreted as the union (limit) of n-th powers of a. In relational structures, this corresponds to reflexive-transitive closure, in language models it is iteration of languages, and so on. Such interpretation of the Kleene star is called *-continuous. However, the usual axiomatization of the Kleene star using induction principles (as opposed to the omega-rule), is essentially weaker and, thus, admits a broader class of models. Existence of nonstandard, non-*-continuous models can be easily proved non-constructively. However, in order to use such models for studying substructural logics with Kleene star one has to construct them explicitly. In this talk, we show two of such models, constructed for proving some facts about derivability in extensions of the Lambek calculus with the Kleene star. Both models are ad hoc algebraic constructions, and we do not yet know whether they could fit in a natural family of models.
The talk is based on my AiML 2018 and AiML 2020 papers
- - - - Wednesday, Nov 25, 2020 - - - -
- - - - Thursday, Nov 26, 2020 - - - -
THANKSGIVING RECESS
- - - - Friday, Nov 27, 2020 - - - -
THANKSGIVING RECESS
Next Week in Logic at CUNY:
- - - - Monday, Nov 30, 2020 - - - -
Logic and Metaphysics Workshop
Date: Monday, November 30, 4.15-6.15 (NY time)
For meeting information, please email: yweiss@gradcenter.cuny.edu Mircea Dumitru (Bucharest)
Title: A Free Logic for Fictionalism
Abstract: In Reference without Referents, Mark Sainsbury aims to provide an account of reference that honours the common-sense view that sentences containing empty names like “Sherlock Holmes”, “Vulcan”, and “Santa Claus” are entirely intelligible, and that many such sentences — “Vulcan doesn’t exist”, “Many children believe that Santa Claus will give them presents at Christmas”, etc.— are literally true. Sainsbury’s account endorses the Davidsonian program in the theory of meaning, and combines this with a commitment to Negative Free Logic, which holds that all simple sentences containing empty names are false. In my talk, I pose a number of problems for this account. In particular, I question the ability of Negative Free Logic to make appropriate sense of the truth of familiar sentences containing empty names, including negative existential claims like “Vulcan doesn’t exist”.
Note: this is based on joint work with Frederick Kroon (Auckland).
- - - - Tuesday, Dec 1, 2020 - - - -
- - - - Wednesday, Dec 2, 2020 - - - -
- - - - Thursday, Dec 3, 2020 - - - -
- - - - Friday, Dec 4, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, Dec 4, 3pm
The seminar will take place virtually at 3pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. Zach Norwood, University of Michigan
TBA
- - - - Other Logic News - - - -
- - - - Web Site - - - -
Find us on the web at:
nylogic.github.io(site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to
jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email
jreitz@nylogic.org.
Barcelona Set Theory Seminar
Barcelona Logic Seminar
11/21/2020 11:38:02
Dear All,
Please find attached the announcement of the next session of the Barcelona Set Theory Seminar. Feel free to distribute it.
SPEAKER: Andrew Brooke-Taylor (Leeds)
TITLE: Categorifying Borel Reducibility
TIME: November 25 at 16:00 (CET)
PLACE: The Seminar will take place online at the following address:
Best regards,
Joan
P.S.: If you do not wish to receive any more announcements, please send an email to
bagaria@ub.edu with the text “Unsubscribe”.
Joan Bagaria
ICREA Research Professor
Universitat de Barcelona
Departament de Matemàtiques i Informàtica
Gran Via de les Corts Catalanes 585
08007 Barcelona
Catalonia
Phone: +34 93 402 1609
Reminder of tomorrow's talk 1 30 pm
Toronto Set Theory Seminar
11/19/2020 13:00:00
Please use the following link and fill the form (every week) to
enter the meeting. This form helps the Field Institute to know
statistical data about attendance.
Speaker: Andrea Medini, University of Vienna
Date and Time: Friday, November 20, 2020 - 1:30pm to 3:00pm
Abstract:
Wadge
theory provides an exhaustive analysis of the topological complexity of
the subsets of a zero-dimensional Polish space. Fons van Engelen
pioneered its applications to topology by obtaining a classification of
the zero-dimensional homogeneous Borel spaces (recall that a space X is homogeneous if for all x,y∈X there exists a homeomorphism h:X⟶X such that h(x)=y).
As a corollary, he showed
that all such spaces (apart from trivial exceptions) are in fact
strongly homogeneous (recall that a space X is strongly homogeneous if all non-empty clopen subspaces of X are homeomorphic to each other).
In a joint work with the other members of the “Wadge Brigade”
(namely, Raphaël Carroy and Sandra Müller), we showed that this last
result extends beyond the Borel realm if one assumes AD. We intend to
sketch the proof of this theorem, with a view towards a complete
classification of the zero-dimensional homogeneous spaces under AD.
Iván Ongay Valverde (he/his)
Andrea Medina talk-Toronto Set Theory Seminar
Toronto Set Theory Seminar
11/16/2020 12:54:27
I send you the information for this week's talk.
Please use the following link and fill the form (every week) to enter the meeting. This form helps the Field Institute to know statistical data about attendance.
Speaker: Andrea Medini, University of Vienna
Date and Time: Friday, November 20, 2020 - 1:30pm to 3:00pm
Abstract:
Wadge
theory provides an exhaustive analysis of the topological complexity of
the subsets of a zero-dimensional Polish space. Fons van Engelen
pioneered its applications to topology by obtaining a classification of
the zero-dimensional homogeneous Borel spaces (recall that a space X is homogeneous if for all x,y∈X there exists a homeomorphism h:X⟶X such that h(x)=y).
As a corollary, he showed that all such spaces (apart from trivial exceptions) are in fact strongly homogeneous (recall that a space X is strongly homogeneous if all non-empty clopen subspaces of X are homeomorphic to each other).
In a joint work with the other members of the “Wadge Brigade”
(namely, Raphaël Carroy and Sandra Müller), we showed that this last
result extends beyond the Borel realm if one assumes AD. We intend to
sketch the proof of this theorem, with a view towards a complete
classification of the zero-dimensional homogeneous spaces under AD.
Next week we will have
Sandra Müller, University of Vienna
Iván Ongay Valverde (he/his)
(KGRC) research seminar talk on Thursday, November 19
Kurt Godel Research Center
11/16/2020 10:41:08
Research seminar
Kurt Gödel Research Center
Thursday, November 19
"Local club condensation in extender models"
Gabriel Fernandes
(Bar-Ilan University, Ramat Gan, Israel)
Local club condensation is a condensation principle defined by Friedman and
Holy. It is a theorem due to Friedman and Holy that local club condensation
holds in most of the extender models that are weakly iterable.
We prove that in any weakly iterable extender model with $\lambda$-indexing,
given a cardinal $\kappa$, the sequence $\langle L_\alpha [E] \mid \alpha <
\kappa^{++} \rangle$ witnesses local club condensation on the interval
$(\kappa^+ , \kappa^{++})$ iff $\kappa$ is not a subcompact cardinal in $L[E]$.
We also prove that if $\kappa$ is subcompact, then there is no sequence
$\langle M_\alpha \mid \alpha < \kappa^{++} \rangle \in L[E]$ with $M_\kappa =
(H_\kappa)^{L[E]}$ and $M_{\kappa^{++}} = (H_{\kappa^{++}})^{L[E]}$ which
witnesses local club condensation in $(\kappa^+ , \kappa^{++})$.
Using the equivalence between subcompact cardinals and $\neg\square_\kappa$,
due to Schimmerling and Zeman, it follows that $\square_\kappa$ holds iff the
sequence $\langle L_\alpha [E] \mid \alpha < \kappa^{++} \rangle$ witnesses
local club condensation on the interval $(\kappa^+ , \kappa^{++})$.
Time and Place
Talk at 3:00pm via Zoom: This talk will be given via Zoom. If you have not
received the meeting link by the day before the talk, please contact
richard.springer@univie.ac.at!
This Week in Logic at CUNY
This Week in Logic at CUNY
11/15/2020 18:30:13
This Week in Logic at CUNY:
- - - - Monday, Nov 16, 2020 - - - -
Logic and Metaphysics Workshop
Date: Monday, November 16, 4.15-6.15 (NY time)
For meeting information, please email: yweiss@gradcenter.cuny.edu Speaker: Nick Stang (Toronto)
Title: Hegel’s Logic as Logic and as Metaphysics
Abstract: In the Encyclopaedia Logic Hegel claims that logic “coincides with” metaphysics (§24). In this talk, I will explain why Hegelian logic (the science of thinking) is identical with metaphysics (the science of being). Along the way, I will also shed light on two of the most obscure aspects of Hegel’s logic: that it involves “movement” and that this movement works by the identification, and resolution, of contradictions.
- - - - Tuesday, Nov 17, 2020 - - - -
Computational Logic Seminar: no meeting on Tuesday November 17
- - - - Wednesday, Nov 18, 2020 - - - -
The New York City
Category Theory Seminar
For meeting zoom details email N. Yanofsky.Speaker: Enrico Ghiorzi, Appalachian State University.
Date and Time: Wednesday November 18, 2020, 7:00 - 8:30 PM., on Zoom.
Title: Internal enriched categories.
Abstract: Internal categories feature a notion of completeness which is remarkably well behaved. For example, the internal adjoint functor theorem requires no solution set condition. Indeed, internal categories are intrinsically small, and thus immune from the size issues commonly afflicting standard category theory. Unfortuntely, they are not quite as expressive as we would like: for example, there is no internal Yoneda lemma. To increase the expressivity of internal category theory, we define a notion of internal enrichment over an internal monoidal category and develop its theory of completeness. The resulting theory unites the good properties of internal categories with the expressivity of enriched category theory, thus providing a powerful framework to work with.
- - - - Thursday, Nov 19, 2020 - - - -
- - - - Friday, Nov 20, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, Nov 20, 3pm
The seminar will take place virtually at 3pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. Philipp Schlicht University of Vienna
The recognisable universe in the presence of measurable cardinals
A set x of ordinals is called recognisable if it is defined, as a singleton, by a formula phi(y) with ordinal parameters that is evaluated in L[y]. The evaluation is always forcing absolute, in contrast to even Sigma_1-formulas with ordinal parameters evaluated in V. Furthermore, this notion is closely related to similar concepts in infinite computation and Hamkins' and Leahy's implicitly definable sets.
It is conjectured that the recognisable universe generated by all recognisable sets is forcing absolute, given sufficient large cardinals. Our goal is thus to determine the recognisable universe in the presence of large cardinals. The new main result, joint with Philip Welch, is a computation of the recognisable universe within the least inner model with infinitely many measurable cardinals.
Next Week in Logic at CUNY:
- - - - Monday, Nov 23, 2020 - - - -
Logic and Metaphysics Workshop
Date: Monday, November 23, 4.15-6.15 (NY time)
For meeting information, please email: yweiss@gradcenter.cuny.edu Behnam Zolghadr (LMU Munich)
Title: How to Abū Hāšim Meinong
Abstract: Similar to Meinong, Abū Hāšim al-Ǧubbāī (d.933), an Islamic theologian/philosopher, held the view that some objects do not exist. This paper is a comparative study between Meinong’s object theory and Abū Hāšim’s theory of nonexistent objects. Our comparative study will be carried out through three main topics: the characterization principle, objecthood, and the ontological status of existence itself. Moreover, Abū Hāšim and his followers argue that the view that some objects do not exist implies some truth value gaps and/or gluts. We will also discuss two of these arguments.
- - - - Tuesday, Nov 24, 2020 - - - -
- - - - Wednesday, Nov 25, 2020 - - - -
- - - - Thursday, Nov 26, 2020 - - - -
THANKSGIVING RECESS
- - - - Friday, Nov 27, 2020 - - - -
THANKSGIVING RECESS
- - - - Other Logic News - - - -
- - - - Web Site - - - -
Find us on the web at:
nylogic.github.io(site designed, built & maintained by Victoria Gitman)
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jreitz@nylogic.org.
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jreitz@nylogic.org.
Barcelona Set Theory Seminar
Barcelona Logic Seminar
11/15/2020 13:04:08
Dear All,
Please find attached the announcement of the next session of the Barcelona Set Theory Seminar. Feel free to distribute it.
SPEAKER: Monroe Eskew (Vienna)
TITLE: Uncommon systems of embeddings
TIME: November 18 at 16:00 (CET)
PLACE: The Seminar will take place online at the following address:
Best regards,
Joan
P.S.: If you do not wish to receive any more announcements, please send an email to
bagaria@ub.edu with the text “Unsubscribe”.
Joan Bagaria
ICREA Research Professor
Universitat de Barcelona
Departament de Matemàtiques i Informàtica
Gran Via de les Corts Catalanes 585
08007 Barcelona
Catalonia
Phone: +34 93 402 1609
Error in Zoom link (seminar tomorrow 11 am)
Toronto Set Theory Seminar
11/12/2020 18:09:22
We had a confusion about the zoom link.
See you tomorrow at 11 am
Iván Ongay Valverde (he/his)
Toronto Set Theory Seminar 11 am (local time) tomorrow Friday 13th
Toronto Set Theory Seminar
11/12/2020 11:00:00
Nov 13th
11:00 am
Ralf Schindler (University of Münster, Germany)
Title: Martin's Maximum^++ implies the P_max axiom (*).
Abstract: Forcing axioms spell out the dictum that if a statement can be
forced, then it is already true. The P_max axiom (*) goes beyond that by
claiming that if a statement is consistent, then it is already true.
Here, the statement in question needs to come from a resticted class of
statements, and "consistent" needs to mean "consistent in a strong
sense." It turns out that (*) is actually equivalent to a forcing axiom,
and the proof is by showing that the (strong) consistency of certain
theories gives rise to a corresponding notion of forcing producing a
model of that theory. This is joint work with D. Asperó building upon
earlier work of R. Jensen and (ultimately) Keisler's "consistency
properties."
Iván Ongay Valverde (he/his)
(KGRC) research seminar talk on Thursday, November 12
Kurt Godel Research Center
11/9/2020 11:39:30
Research seminar
Kurt Gödel Research Center
Thursday, November 12
"Can You Take Komjath's Inaccessible Away?"
Hossein Lamei Ramandi
(University of Toronto, Ontario, Canada)
In this talk we aim to compare Kurepa trees and Aronszajn trees. Moreover, we
talk about the affect of large cardinal assumptions on this comparison. Using
the the method of walks on ordinals, we will show it is consistent with ZFC
that there is a Kurepa tree and every Kurepa tree contains a Souslin subtree,
if there is an inaccessible cardinal. This is stronger than Komjath's theorem
which asserts the same consistency from two inaccessible cardinals. We will
briefly sketch the ideas to prove that our large cardinal assumption is
optimal. If time permits, we talk about the comparison of Kurepa trees and
Aronszajn trees in the presence of no large cardinal.
This is a joint work with Stevo Todorcevic.
Time and Place
Talk at 3:00pm via Zoom: This talk will be given via Zoom. If you have not
received the meeting link by the day before the talk, please contact
richard.springer@univie.ac.at!
This Week in Logic at CUNY
This Week in Logic at CUNY
11/8/2020 21:50:45
This Week in Logic at CUNY:
- - - - Monday, Nov 9, 2020 - - - -
Logic and Metaphysics Workshop
Date: Monday, November 9, 4.15-6.15 (NY time)
For meeting information, please email: yweiss@gradcenter.cuny.edu Eoin Moore (CUNY)
Title: Towards a Justification Logic for FDE
Abstract: In this work-in-progress, I aim to develop a justification logic counterpart to first degree entailment. I produce a logic which is an extension of FDE using justification terms. The results are extended to other paraconsistent logics.
- - - - Tuesday, Nov 10, 2020 - - - -
Computational Logic Seminar
Tuesday, Nov 10, 2-4pm
Speaker: Daniel Rogozin, Institute for Information Transmission Problems, Russian Academy of Sciences
Title: Categorical and algebraic aspects of the intuitionistic modal logic IEL^-
Abstract: The intuitionistic modal logic IEL^- is a formalisation of intuitionistic beliefs. This logic has been introduced by S. Artemov and T. Protopopescu to provide an intuitionistic view of knowledge agreed with BHK-semantics. One may understand the modal axioms of this logic in computational terms. Such a consideration is of interest for functional programming theory. We construct the modal lambda calculus based Curry-Howard isomorphic to IEL^- and show that this calculus has strong normalisation and Church-Rosser properties. We have a look at categorical semantics of the obtained lambda calculus and see that it is complete with respect to Cartesian closed categories with certain endofunctors.
Algebraically, the IEL^- modality is a prenucleus operator widespread in the theory of locales and point-free topology. We consider predicate extensions of IEL^- (and some similar logics) and provide a sort of Kripke-Joyal semantics for those logics developing several ideas by R. Goldblatt. We show that such intuitionistic predicate modal logics are complete with respect to their cover systems with the Dedekind-MacNeille completion and the representation of Heyting algebras with corresponding operators.
- - - - Wednesday, Nov 11, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, Nov 11, 12:00pm
The seminar will take place virtually at 12pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Joel David Hamkins, Oxford University
Continuous models of arithmetic
Ali Enayat had asked whether there is a model of Peano arithmetic (PA) that can be represented as ⟨Q,⊕,⊗⟩⟨Q,⊕,⊗⟩, where ⊕⊕ and ⊗⊗ are continuous functions on the rationals QQ. We prove, affirmatively, that indeed every countable model of PA has such a continuous presentation on the rationals. More generally, we investigate the topological spaces that arise as such topological models of arithmetic. The reals RR, the reals in any finite dimension RnRn, the long line and the Cantor space do not, and neither does any Suslin line; many other spaces do; the status of the Baire space is open.
This is joint work with Ali Enayat, myself and Bartosz Wcisło.
- - - - Thursday, Nov 12, 2020 - - - -
- - - - Friday, Nov 13, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, Nov 13, 3pm
The seminar will take place virtually at 3pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. Diana Montoya, University of Vienna
Independence and uncountable cardinals
The classical concept of independence, first introduced by Fichtenholz and Kantorovic has been of interest within the study of combinatorics of the subsets of the real line. In particular the study of the cardinal characteristic ii defined as the minimum size of a maximal independent family of subsets of ω.ω. In the first part of the talk, we will review the basic theory, as well as the most important results regarding the independence number. We will also point out our construction of a poset PP forcing a maximal independent family of minimal size which turns out to be indestructible after forcing with a countable support iteration of Sacks forcing.
In the second part, we will talk about the generalization (or possible generalizations) of the concept of independence in the generalized Baire spaces, i.e. within the space κκκκ when κκ is a regular uncountable cardinal and the new challenges this generalization entails. Moreover, for a specific version of generalized independence, we can have an analogous result to the one mentioned in the paragraph above.
This is joint work with Vera Fischer.
Next Week in Logic at CUNY:
- - - - Monday, Nov 16, 2020 - - - -
Logic and Metaphysics Workshop
Date: Monday, November 16, 4.15-6.15 (NY time)
For meeting information, please email: yweiss@gradcenter.cuny.edu Speaker: Nick Stang
- - - - Tuesday, Nov 17, 2020 - - - -
- - - - Wednesday, Nov 18, 2020 - - - -
- - - - Thursday, Nov 19, 2020 - - - -
- - - - Friday, Nov 20, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, Nov 20, 3pm
The seminar will take place virtually at 3pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. Philipp Schlicht University of Vienna
TBA
- - - - Other Logic News - - - -
- - - - Web Site - - - -
Find us on the web at:
nylogic.github.io(site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to
jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email
jreitz@nylogic.org.
Barcelona Set Theory Seminar
Barcelona Logic Seminar
11/8/2020 15:20:36
Dear All,
Please find attached the announcement of the next session of the Barcelona Set Theory Seminar. Feel free to distribute it.
SPEAKER: Gabriel Goldberg (UC Berkeley)
TITLE: On the uniqueness of elementary embeddings
TIME: 16:00 (CET)
PLACE: The Seminar will take place online at the following address:
Best regards,
Joan
P.S.: If you do not wish to receive any more announcements, please send an email to
bagaria@ub.edu with the text “Unsubscribe”.
Joan Bagaria
ICREA Research Professor
Universitat de Barcelona
Departament de Matemàtiques i Informàtica
Gran Via de les Corts Catalanes 585
08007 Barcelona
Catalonia
Phone: +34 93 402 1609
Seminar at 11 am (Friday 13th) and back to normal following week
Toronto Set Theory Seminar
11/6/2020 15:39:46
Hello all,
I send you the announcement for the following two talks. Notice the unusual time for next week.
Nov 13th
11:00 am
Ralf Schindler (University of Münster, Germany)
Title: Martin's Maximum^++ implies the P_max axiom (*).
Abstract: Forcing axioms spell out the dictum that if a statement can be
forced, then it is already true. The P_max axiom (*) goes beyond that by
claiming that if a statement is consistent, then it is already true.
Here, the statement in question needs to come from a resticted class of
statements, and "consistent" needs to mean "consistent in a strong
sense." It turns out that (*) is actually equivalent to a forcing axiom,
and the proof is by showing that the (strong) consistency of certain
theories gives rise to a corresponding notion of forcing producing a
model of that theory. This is joint work with D. Asperó building upon
earlier work of R. Jensen and (ultimately) Keisler's "consistency
properties."
--
Nov 20th
1:30 pm
Andrea Medini (University of Vienna, Austria)
Title: Topological applications of Wadge theory
Abstract: Wadge theory provides an exhaustive analysis of the
topological complexity of the subsets of a zero-dimensional Polish
space. Fons van Engelen pioneered its applications to topology by
obtaining a classification of the zero-dimensional homogeneous Borel
spaces (recall that a space $X$ is homogeneous if for all $x,y\in X$
there exists a homeomorphism $h:X\longrightarrow X$ such that $h(x)=y$).
As a corollary, he showed that all such spaces (apart from trivial
exceptions) are in fact strongly homogeneous (recall that a space $X$ is
strongly homogeneous if all non-empty clopen subspaces of $X$ are
homeomorphic to each other).
In a joint work with the other members of the “Wadge Brigade” (namely,
Raphaël Carroy and Sandra Müller), we showed that this last result
extends beyond the Borel realm if one assumes AD. We intend to sketch
the proof of this theorem, with a view towards a complete classification
of the zero-dimensional homogeneous spaces under AD.
Iván Ongay Valverde (he/his)
Reminder: Toronto Set Theory Seminar Talk Today (in 15 minutes)
Toronto Set Theory Seminar
11/6/2020 13:15:38
Nov 6th 1:30 pm
Jonathan Schilhan (University of Vienna, Austria)
Title: Definable maximal families of reals in forcing extensions
Abstract: Many types of combinatorial, algebraic or measure-theoretic
families of reals, such as mad families, Hamel bases or Vitali sets, can
be framed as maximal independent sets in analytic hypergraphs on Polish
spaces. Their existence is guaranteed by the Axiom of Choice, but
low-projective witnesses ($\mathbf{Delta}^1_2$) were only known to exist
in general in models of the form $L[a]$ for a real $a$. Our main result
is that, after a countable support iteration of Sacks forcing or for
example splitting forcing (a less known forcing adding splitting reals)
over L, every analytic hypergraph on a Polish space has a
$\mathbf{\Delta}^1_2$ maximal independent set. As a corollary, this
solves an open problem of Brendle, Fischer and Khomskii by providing a
model with a $\Pi^1_1$ mif (maximal independent family) while the
independence number $\mathfrak{i}$ is bigger than $\aleph_1$.
Thanks for your patience. Due to technical errors, the zoom link was generated really late. See you soon!!!!!!!!!!!
Iván Ongay Valverde (he/his)
Logic Seminar 11 Nov 2020 17:00 hrs at NUS by Philipp Schlicht
NUS Logic Seminar
11/5/2020 20:00:42
Invitation to the Logic Seminar at the National University of Singapore
Date: Wednesday, 11 Nov 2020, 17:00 hrs
Talk via Zoom: https://nus-sg.zoom.us/j/96860201432?pwd=cVdwZmd2clVFaEhaTmJjaGdXMFdmdz09
Meeting ID: 968 6020 1432
Password: Is P=NP?
Speaker: Philipp Schlicht, University of Vienna
Title: Structural results about Pi^1_1 and Sigma^1_2 sets
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Abstract: Similarities between c.e., Pi^1_1 and Sigma^1_2 sets can be
explained by representing Pi^1_1 and Sigma^1_2 sets as c.e. with respect to
a transfinite enumeration procedure. This representation is important for
classical results about Pi^1_1 and Sigma^1_2 sets, but also for recent
results, for instance about randomness at the level of Pi^1_1 by Hjorth and
Nies and structural results about Sigma^1_2 sets by Chong, Wu and Yu.
In the main result, we calculate the lengths of enumerations. More
precisely, we isolate a certain countable ordinal tau and show that the
length of an enumeration of a Pi^1_1 or Sigma^1_2 set either equals omega_1
or is below tau, and tau is optimal. This ordinal has many other
interesting characterisations. For example, we show that tau is the optimal
bound for the countable ranks of wellfounded Sigma^1_2 relations, in
analogy with the Kunen-Martin theorem. We will further touch on related
structural problems such as calculating Borel ranks of Pi^1_1 and Sigma^1_2
Borel sets.
This is joint work with Philip Welch and Merlin Carl.
Matt Foreman: Hilbert's 10th problem for dynamical systems
Boise Logic and Set Theory Seminar
11/4/2020
Please join us for the next meeting of the ELASTIC seminar next Tuesday, November 10, at 3pm. The meeting will take place at https://boisestate.zoom.us/j/98755933038.
Speaker: Matt Foreman (UCI)
Title: Hilbert's 10th problem for dynamical systems
Abstract: A basic problem in smooth dynamics is determining if a system can be distinguished from its inverse, i.e., whether a smooth diffeomorphism T is isomorphic to T^{-1}. We show that this problem is sufficiently general that asking it for particular choices of T is equivalent to the validity of well-known number theoretic conjectures including the Riemann Hypothesis and Goldbach's conjecture. Further one can produce computable diffeomorphisms T such that the question of whether T is isomorphic to T^{-1} is independent of ZFC.
Tagged: Matt Foreman
(KGRC) research seminar talk on Thursday, November 5
Kurt Godel Research Center
11/2/2020 11:16:29
Research seminar
Kurt Gödel Research Center
Thursday, November 5
"On Continuous Tree-Like Scales and related properties of Internally
Approachable structures"
Omer Ben-Neria
(Hebrew University of Jerusalem, Israel)
In his PhD thesis, Luis Pereira isolated and developed several principles
of singular cardinals that emerge from Shelah's PCF theory; principles
which involve properties of scales, such as the inexistence of continuous
Tree-Like scales, and properties of internally approachable structures
such as the Approachable Free Subset Property.
In the talk, we will discuss these principles and their relations, and
present new results from a joint work with Dominik Adolf concerning their
consistency and consistency strength.
Time and Place
Talk at 3:00pm via Zoom:
This talk will be given via Zoom. If you haven't received the meeting link
by the day before the talk, please contact richard.springer@univie.ac.at!
Tagged: Omer Ben-Neria
Logic Seminar 4 Nov 2020 17:00 hrs at NUS by Andre Nies
NUS Logic Seminar
11/2/2020 0:34:00
Invitation to the Logic Seminar at the National University of Singapore
Date: Wednesday, 4 Nov 2020, 17:00 hrs
Talk via Zoom: https://nus-sg.zoom.us/j/96860201432?pwd=cVdwZmd2clVFaEhaTmJjaGdXMFdmdz09
Meeting ID: 968 6020 1432
Password: Is P=NP?
Speaker: Andre Nies, University of Auckland
Title: Weak reducibilities on the K-trivial sets
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Abstract:
Abstract: The K-trivial sets are antirandom in the sense that the
initial segment complexity in terms of prefix-free Kolmogorov
complexity K grows as slowly as possible. Chaitin introduced this
notion in about 1975, and showed that each K-trivial is Turing below
the halting set. Shortly after, Solovay proved that a K-trivial set
can be noncomputable.
In the past two decades, many alternative characterisations of this
class have been found: properties such as being low for K, low for
Martin-Loef (ML) randomness, and a basis for ML randomness, which
state in one way or the other that the set is close to computable.
Initially, the class of noncomputable K-trivials appeared to be
amorphous. More recently, evidence of an internal structure has been
found. Most of these results can be phrased in the language of a
mysterious reducibility on the K-trivials which is weaker than
Turing's: A is ML-below B if each ML-random computing B also computes A.
Bienvenu, Greenberg, Kucera, Nies and Turetsky (JEMS 2016) showed that
there an ML-complete K-trivial set. Greenberg, Miller and Nies (JML,
2019) established a dense hierarchy of subclasses of the K-trivials
based on fragments of Omega computing the set, and each such subclass
is an initial segment for ML. More recent results generalise these
approaches using so-called cost functions. They also show that each
K-trivial set is ML-equivalent to a c.e. K-trivial.
Alternative reducibilities on the K-trivials will be considered near
the end of the talk. One of them is related to the extreme lowness
notion of strong jump traceability, and appears to be orthogonal to
ML-reducibility. Very recent work with Greenberg and Turetsky provides
manyfold characterisations in terms of cost functions, and random oracles.
Tagged: Andre Nies
This Week in Logic at CUNY
This Week in Logic at CUNY
11/1/2020 21:03:08
This Week in Logic at CUNY:
- - - - Monday, Nov 2, 2020 - - - -
Logic and Metaphysics Workshop
Date: Monday, November 2, 4.15-6.15 (NY time)
For meeting information, please email: yweiss@gradcenter.cuny.edu Speaker: Heinrich Wansing (Bochum)
Title: A Note on Synonymy in Proof-Theoretic Semantics
Abstract: The topic of identity of proofs was put on the agenda of general (or structural) proof theory at an early stage. The relevant question is: When are the differences between two distinct proofs (understood as linguistic entities, proof figures) of one and the same formula so inessential that it is justified to identify the two proofs? The paper addresses another question: When are the differences between two distinct formulas so inessential that these formulas admit of identical proofs? The question appears to be especially natural if the idea of working with more than one kind of derivations is taken seriously. If a distinction is drawn between proofs and disproofs (or refutations) as primitive entities, it is quite conceivable that a proof of one formula amounts to a disproof of another formula, and vice versa. The paper develops this idea.
- - - - Tuesday, Nov 3, 2020 - - - -
Computational Logic Seminar
Tuesday, Nov 3, 2-4pm
For meeting zoom details please email sartemov@gmail.com.
Speaker: Sergei Artemov, Graduate Center CUNY Title: Justification Awareness Models
Abstract: We offer a new approach in formal epistemology which overcomes some principal deficiencies of Hintikka-style modal epistemic logic such as logical omniscience, a hidden assumption of the common knowledge of the model, missing evidence representation, etc.
In this project, we pursue two principal ideas: (i) justifications are prime objects of epistemic modeling: knowledge and belief are defined evidence-based concepts; (ii) awareness restrictions are applied to justifications rather than to propositions, which allows for the maintaining of desirable closure properties. The basic resulting structures, Justification Awareness Models, JAMs, naturally include major justification models, Kripke models and, in addition, represent situations with multiple possibly fallible justifications which, in full generality, were previously off the scope of rigorous epistemic modeling.
- - - - Wednesday, Nov 4, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, Oct 28, 3:00pm
The seminar will take place virtually at 3pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Victoria Gitman, CUNY
A model of second-order arithmetic satisfying AC but not DC: Part II
One of the strongest second-order arithmetic systems is full second-order arithmetic Z2Z2 which asserts that every second-order formula (with any number of set quantifiers) defines a set. We can augment Z2Z2 with choice principles such as the choice scheme and the dependent choice scheme. The Σ1nΣn1-choice scheme asserts for every Σ1nΣn1-formula φ(n,X)φ(n,X) that if for every nn, there is a set XX witnessing φ(n,X)φ(n,X), then there is a single set ZZ whose nn-th slice ZnZn is a witness for φ(n,X)φ(n,X). The Σ1nΣn1-dependent choice scheme asserts that every Σ1nΣn1-relation φ(X,Y)φ(X,Y) without terminal nodes has an infinite branch: there is a set ZZ such that φ(Zn,Zn+1)φ(Zn,Zn+1) holds for all nn. The system Z2Z2 proves the Σ12Σ21-choice scheme and the Σ12Σ21-dependent choice scheme. The independence of Π12Π21-choice scheme from Z2Z2 follows by taking a model of Z2Z2 whose sets are the reals of the Feferman-Levy model of ZFZF in which every ℵLnℵnL is countable and ℵLωℵωL is the first uncountable cardinal.
We construct a model of ZF+ACωZF+ACω whose reals give a model of Z2Z2 together with the full choice scheme in which Π12Π21-dependent choice fails. This result was first proved by Kanovei in 1979 and published in Russian. It was rediscovered by Sy Friedman and myself with a slightly simplified proof.
- - - - Thursday, Nov 5, 2020 - - - -
Philog - Seminar in Logic, Games and Philosophy
On Thursday, November 5 (6:30 PM) we will return to the book by Diaconis and Skyrms . The Zoom talk will be led by Paul Pedersen.
Title: Inverse Inference from Bayes and Laplace to Statistics.
Abstract: You are screening new drugs for a certain disease. Some patients get better by at least a certain amount; some don't. For one new drug, more get better on the drug than on a placebo. How confident should you be of the new drug's effectiveness on the evidence?
A Zoom link will be posted on the webpage
https://philog.arthurpaulpedersen.org/ - - - - Friday, Nov 6, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, Nov 6, 3pm
The seminar will take place virtually at 3pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. Ernest Schimmerling, Carnegie Mellon UniversityCovering at limit cardinals of K
Theorem (Mitchell and Schimmerling, submitted for publication) Assume there is no transitive class model of ZFC with a Woodin cardinal. Let νν be a singular ordinal such that ν>ω2ν>ω2 and cf(ν)<|ν|cf(ν)<|ν|. Suppose νν is a regular cardinal in K. Then νν is a measurable cardinal in K. Moreover, if cf(ν)>ωcf(ν)>ω, then oK(ν)≥cf(ν)oK(ν)≥cf(ν).
I will say something intuitive and wildly incomplete but not misleading about the meaning of the theorem, how it is proved, and the history of results behind it.
Next Week in Logic at CUNY:
- - - - Monday, Nov 9, 2020 - - - -
Logic and Metaphysics Workshop
Date: Monday, November 9, 4.15-6.15 (NY time)
For meeting information, please email: yweiss@gradcenter.cuny.edu Eoin Moore (CUNY)
Title: Towards a Justification Logic for FDE
Abstract: In this work-in-progress, I aim to develop a justification logic counterpart to first degree entailment. I produce a logic which is an extension of FDE using justification terms. The results are extended to other paraconsistent logics.
- - - - Tuesday, Nov 10, 2020 - - - -
- - - - Wednesday, Nov 11, 2020 - - - -
- - - - Thursday, Nov 12, 2020 - - - -
- - - - Friday, Nov 13, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, Nov 13, 3pm
The seminar will take place virtually at 3pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. Diana Montoya, University of Vienna
TBA
- - - - Other Logic News - - - -
- - - - Web Site - - - -
Find us on the web at:
nylogic.github.io(site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to
jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email
jreitz@nylogic.org.
Seminar next week
Toronto Set Theory Seminar
10/30/2020 15:54:27
Hello everyone,
Here a list for upcoming talk (I had a typo last week,
Ralf Schindle's talk will be the third one in Nov 13th). Links will be provided later.
Nov 6th 1:30 pm
Jonathan Schilhan (University of Vienna, Austria)
Title: Definable maximal families of reals in forcing extensions
Abstract: Many types of combinatorial, algebraic or measure-theoretic
families of reals, such as mad families, Hamel bases or Vitali sets, can
be framed as maximal independent sets in analytic hypergraphs on Polish
spaces. Their existence is guaranteed by the Axiom of Choice, but
low-projective witnesses ($\mathbf{Delta}^1_2$) were only known to exist
in general in models of the form $L[a]$ for a real $a$. Our main result
is that, after a countable support iteration of Sacks forcing or for
example splitting forcing (a less known forcing adding splitting reals)
over L, every analytic hypergraph on a Polish space has a
$\mathbf{\Delta}^1_2$ maximal independent set. As a corollary, this
solves an open problem of Brendle, Fischer and Khomskii by providing a
model with a $\Pi^1_1$ mif (maximal independent family) while the
independence number $\mathfrak{i}$ is bigger than $\aleph_1$.
-----
Nov 13th
11:00 am
Ralf Schindler (University of Münster, Germany)
Title: Martin's Maximum^++ implies the P_max axiom (*).
Abstract: Forcing axioms spell out the dictum that if a statement can be
forced, then it is already true. The P_max axiom (*) goes beyond that by
claiming that if a statement is consistent, then it is already true.
Here, the statement in question needs to come from a resticted class of
statements, and "consistent" needs to mean "consistent in a strong
sense." It turns out that (*) is actually equivalent to a forcing axiom,
and the proof is by showing that the (strong) consistency of certain
theories gives rise to a corresponding notion of forcing producing a
model of that theory. This is joint work with D. Asperó building upon
earlier work of R. Jensen and (ultimately) Keisler's "consistency
properties."
------
Nov 20th
1:30 pm
Andrea Medini (University of Vienna, Austria)
Title: Topological applications of Wadge theory
Abstract: Wadge theory provides an exhaustive analysis of the
topological complexity of the subsets of a zero-dimensional Polish
space. Fons van Engelen pioneered its applications to topology by
obtaining a classification of the zero-dimensional homogeneous Borel
spaces (recall that a space $X$ is homogeneous if for all $x,y\in X$
there exists a homeomorphism $h:X\longrightarrow X$ such that $h(x)=y$).
As a corollary, he showed that all such spaces (apart from trivial
exceptions) are in fact strongly homogeneous (recall that a space $X$ is
strongly homogeneous if all non-empty clopen subspaces of $X$ are
homeomorphic to each other).
In a joint work with the other members of the “Wadge Brigade” (namely,
Raphaël Carroy and Sandra Müller), we showed that this last result
extends beyond the Borel realm if one assumes AD. We intend to sketch
the proof of this theorem, with a view towards a complete classification
of the zero-dimensional homogeneous spaces under AD.
-----
Nov 27th
1:30 pm
Sandra Müller (University of Vienna, Austria)
Title: TBA
Iván Ongay Valverde (he/his)
Tagged: Jonathan Schilhan
Seminar Today reminder (in half an hour)
Toronto Set Theory Seminar
10/30/2020 13:01:45
In a couple of minutes we will have:
Speaker: Spencer Unger
Title: Reflection properties at successors of singulars.
Abstract: We
survey some recent advances in techniques for getting reflection
properties at successors of singulars with particular attention to the
tree property and stationary reflection
Iván Ongay Valverde (he/his)
Tagged: Spencer Unger
Barcelona Set Theory Seminar
Barcelona Logic Seminar
10/30/2020 10:46:25
Dear All,
Please find attached the announcement of the next session of the Barcelona Set Theory Seminar. Feel free to distribute it.
SPEAKER: Giorgio Venturi (University of Campinas)
TITLE: On non-classical models of ZFC
TIME: 416:00 (CET)
PLACE: The Seminar will take place at the following address:
Best regards,
Joan
P.S.: If you do not wish to receive any more announcements, please send an email to
bagaria@ub.edu with the text “Unsubscribe”.
Joan Bagaria
ICREA Research Professor
Universitat de Barcelona
Departament de Matemàtiques i Informàtica
Gran Via de les Corts Catalanes 585
08007 Barcelona
Catalonia
Phone: +34 93 402 1609
Tagged: Giorgio Venturi
(KGRC) research seminar talk on Thursday, October 29
Kurt Godel Research Center
10/26/2020 11:51:12
Research seminar
Kurt Gödel Research Center
Thursday, October 29
"Structural reflection and shrewd cardinals"
Philipp Lücke
(University of Barcelona, Spain)
In my talk, I want to present work dealing with the interplay between Time
and Place extensions of the \emph{Downward Löwenheim–Skolem Theorem} to
strong logics, large cardinal axioms and set-theoretic reflection
principles, focussing on the characterization of large cardinal notions
through model- and set-theoretic reflection properties. The work of
Bagaria and his collaborators shows that various important objects in the
middle and upper reaches of the large cardinal hierarchy can be
characterized through principles of \emph{structural reflection}. I will
discuss recent results dealing with possible characterizations of notions
from the lower part of this hierarchy through the principle
$\mathrm{SR}^-$, introduced by Bagaria and Väänänen. These results show
that the principle $\mathrm{SR}^-$ is closely connected to the notion of
\emph{shrewd cardinals}, introduced by Rathjen in a proof-theoretic
context, and embedding characterizations of these cardinals that resembles
Magidor's classical characterization of supercompactness.
Time and Place
This talk will be given via Zoom. If you haven't received the meeting link
by the day before the talk, please contact richard.springer@univie.ac.at!
Tagged: Philipp Lücke
Toronto Set Theory Seminar (First talk of this Term)
Toronto Set Theory Seminar
10/25/2020 11:17:04
Hello Everyone,
The Toronto Set Theory seminar will finally start this semester. The organizer will be organized by two post-docs, ad tradition dictates: David Schrittesser (U-Toronto, cc'ed) and me (Ivan Ongay-Valverde,
York).
The first talk of the semester will be given by Spencer Unger who recently moved to Toronto. After that, we will have weekly talks. The second talk will be given by
Ralf Schindler from Münste. Here the information:
Speaker: Spencer Unger
Title:
Reflection properties at successors of singulars.
Abstract:
We survey some recent advances in techniques for getting reflection
properties at successors of singulars with particular attention to the
tree property and stationary reflection
For the second talk
Speaker:
Ralf Schindler
Time and link: Nov 6, 2020 11:00 AM
Eastern Time (US and Canada, i.e.
Toronto time
)
Title: TBA
Abstract: TBA
See you in "a week"
Best
Iván Ongay Valverde (he/his)
Tagged: Spencer Unger
This Week in Logic at CUNY
This Week in Logic at CUNY
10/25/2020 22:11:38
This Week in Logic at CUNY:
- - - - Monday, Oct 26, 2020 - - - -
Logic and Metaphysics Workshop
Date: Monday, October 26th, 4.15-6.15 (NY time)
For meeting information, please email: yweiss@gradcenter.cuny.edu Speaker: Lisa Warenski (CUNY)
Title: The Metaphysics of Epistemic Norms
Abstract: A metanormative theory inter alia gives an account of the objectivity of normative claims and addresses the ontological status of normative properties in its target domain. A metanormative theory will thus provide a framework for interpreting the claims of its target first-order theory. Some irrealist metanormative theories (e.g., Gibbard 1990 and Field 2000, 2009) conceive of normative properties as evaluative properties that may attributed to suitable objects of assessment (doxastic states, agents, or actions) in virtue of systems of norms. But what are the conditions for the acceptability of systems of norms, and relatedly, correctness of normative judgment? In this paper, I take up these questions for epistemic norms. Conditions for the acceptability of epistemic norms, and hence correctness of epistemic judgment, will be based on the critical evaluation of norms for their ability to realize our epistemic aims and values. Epistemic aims and values, in turn, are understood to be generated from the epistemic point of view, namely the standpoint of valuing truth.
- - - - Tuesday, Oct 27, 2020 - - - -
Computational Logic Seminar
Speaker: John Connor, Graduate Center CUNY
Title: Justification Logics as Internal Languages -- Part 2 of 2
Abstract:
In this talk the justification logic J- is shown to correspond to the internal language of a class of categories. In addition to proving soundness and completeness, we will show that the categorical models and the basic models are in correspondence, and that one can be transformed into the other in a straightforward way.
- - - - Wednesday, Oct 28, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, Oct 28, 3:00pm
The seminar will take place virtually at 3pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Victoria Gitman, CUNY
A model of second-order arithmetic satisfying AC but not DC
One of the strongest second-order arithmetic systems is full second-order arithmetic Z2Z2 which asserts that every second-order formula (with any number of set quantifiers) defines a set. We can augment Z2Z2 with choice principles such as the choice scheme and the dependent choice scheme. The Σ1nΣn1-choice scheme asserts for every Σ1nΣn1-formula φ(n,X)φ(n,X) that if for every nn, there is a set XX witnessing φ(n,X)φ(n,X), then there is a single set ZZ whose nn-th slice ZnZn is a witness for φ(n,X)φ(n,X). The Σ1nΣn1-dependent choice scheme asserts that every Σ1nΣn1-relation φ(X,Y)φ(X,Y) without terminal nodes has an infinite branch: there is a set ZZ such that φ(Zn,Zn+1)φ(Zn,Zn+1) holds for all nn. The system Z2Z2 proves the Σ12Σ21-choice scheme and the Σ12Σ21-dependent choice scheme. The independence of Π12Π21-choice scheme from Z2Z2 follows by taking a model of Z2Z2 whose sets are the reals of the Feferman-Levy model of ZFZF in which every ℵLnℵnL is countable and ℵLωℵωL is the first uncountable cardinal.
We construct a model of ZF+ACωZF+ACω whose reals give a model of Z2Z2 together with the full choice scheme in which Π12Π21-dependent choice fails. This result was first proved by Kanovei in 1979 and published in Russian. It was rediscovered by Sy Friedman and myself with a slightly simplified proof.
- - - - Thursday, Oct 29, 2020 - - - -
Seminar in Logic, Games and Philosophy
Zoom seminar, Thursday October 29 at 6:30 PM
Cailin O'Connor, UC Irvine
Title: Measuring Conventionality
Abstract: Standard accounts of convention include notions of arbitrariness. But many have conceived of conventionality as an all or nothing affair. In this paper, I develop a framework for thinking of conventions as coming in degrees of arbitrariness. In doing so, I introduce an information theoretic measure intended to capture the degree to which a solution to a certain social problem could have been otherwise. As the paper argues, this framework can help improve explanation aimed at the cultural evolution of social traits. Good evolutionary explanations recognize that most functional traits are also conventional, at least to some degree, and vice versa.
A zoom link will be posted on Wednesday at
https://philog.arthurpaulpedersen.org/
- - - - Friday, Oct 30, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, Oct 30, 3pm
The seminar will take place virtually at 3pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. Benedikt Löwe, University of Hamburg
TBA
Workshop on Substructural Logics, Hierarchies Thereof, and Solutions to the Liar
The Logic and Metaphysics Workshop and the Saul Kripke Center are hosting a day of talks on substructural Logics, hierarchies thereof, and solutions to the Liar on Friday, October 30, 2020. The schedule, NY time, will be as follows (abstracts can be accessed
here):
10.00. Strict/Tolerant and Tolerant/Strict Logics, Melvin Fitting, CUNY.
11.40. Expressibility and the (Un)paradoxicality Paradoxes, Will Nava, NYU.
1.20. Lunch Break.
2.00. What is Meta-inferential Validity?, Chris Scambler, NYU.
3.40. Supervaluations and the Strict-Tolerant Hierarchy, Brian Porter, CUNY.
5.20. End (virtual gathering).
Talks will be on Zoom, and are open to all interested. A link will be sent out on the mailing lists of the Logic and Metaphysics Workshop and the Saul Kripke Center the day before. People not on either of those lists who want to receive the link should email Graham Priest (priest DOT graham AT gmail DOT com). PLEASE FEEL FREE TO PASS ON THIS ANNOUNCEMENT.
Next Week in Logic at CUNY:
- - - - Monday, Nov 2, 2020 - - - -
Logic and Metaphysics Workshop
Date: Monday, November 2, 4.15-6.15 (NY time)
For meeting information, please email: yweiss@gradcenter.cuny.edu Speaker: Lisa Warenski (CUNY).
Title: The Metaphysics of Epistemic Norms
Abstract: A metanormative theory inter alia gives an account of the objectivity of normative claims and addresses the ontological status of normative properties in its target domain. A metanormative theory will thus provide a framework for interpreting the claims of its target first-order theory. Some irrealist metanormative theories (e.g., Gibbard 1990 and Field 2000, 2009) conceive of normative properties as evaluative properties that may attributed to suitable objects of assessment (doxastic states, agents, or actions) in virtue of systems of norms. But what are the conditions for the acceptability of systems of norms, and relatedly, correctness of normative judgment? In this paper, I take up these questions for epistemic norms. Conditions for the acceptability of epistemic norms, and hence correctness of epistemic judgment, will be based on the critical evaluation of norms for their ability to realize our epistemic aims and values. Epistemic aims and values, in turn, are understood to be generated from the epistemic point of view, namely the standpoint of valuing truth.
- - - - Tuesday, Nov 3, 2020 - - - -
- - - - Wednesday, Nov 4, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, Oct 28, 3:00pm
The seminar will take place virtually at 3pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Victoria Gitman, CUNY
A model of second-order arithmetic satisfying AC but not DC: Part II
One of the strongest second-order arithmetic systems is full second-order arithmetic Z2Z2 which asserts that every second-order formula (with any number of set quantifiers) defines a set. We can augment Z2Z2 with choice principles such as the choice scheme and the dependent choice scheme. The Σ1nΣn1-choice scheme asserts for every Σ1nΣn1-formula φ(n,X)φ(n,X) that if for every nn, there is a set XX witnessing φ(n,X)φ(n,X), then there is a single set ZZ whose nn-th slice ZnZn is a witness for φ(n,X)φ(n,X). The Σ1nΣn1-dependent choice scheme asserts that every Σ1nΣn1-relation φ(X,Y)φ(X,Y) without terminal nodes has an infinite branch: there is a set ZZ such that φ(Zn,Zn+1)φ(Zn,Zn+1) holds for all nn. The system Z2Z2 proves the Σ12Σ21-choice scheme and the Σ12Σ21-dependent choice scheme. The independence of Π12Π21-choice scheme from Z2Z2 follows by taking a model of Z2Z2 whose sets are the reals of the Feferman-Levy model of ZFZF in which every ℵLnℵnL is countable and ℵLωℵωL is the first uncountable cardinal.
We construct a model of ZF+ACωZF+ACω whose reals give a model of Z2Z2 together with the full choice scheme in which Π12Π21-dependent choice fails. This result was first proved by Kanovei in 1979 and published in Russian. It was rediscovered by Sy Friedman and myself with a slightly simplified proof.
- - - - Thursday, Nov 5, 2020 - - - -
- - - - Friday, Nov 6, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, Oct 30, 3pm
The seminar will take place virtually at 3pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
- - - - Other Logic News - - - -
- - - - Web Site - - - -
Find us on the web at:
nylogic.github.io(site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to
jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email
jreitz@nylogic.org.
Barcelona Set Theory Seminar
Barcelona Logic Seminar
10/25/2020 10:26:58
Dear All,
Please find attached the announcement of the next session of the Barcelona Set Theory Seminar. Feel free to distribute it.
The Seminar will take place at the following address:
Best regards,
Joan
P.S.: If you do not wish to receive any more announcements, please send an email to
bagaria@ub.edu with the text “Unsubscribe”.
Joan Bagaria
ICREA Research Professor
Universitat de Barcelona
Departament de Matemàtiques i Informàtica
Gran Via de les Corts Catalanes 585
08007 Barcelona
Catalonia
Phone: +34 93 402 1609
(KGRC) research seminar talk on Thursday, October 22
Kurt Godel Research Center
10/19/2020 10:55:49
Research seminar
Kurt Gödel Research Center
Thursday, October 22
"Tree forcings, sharps and absoluteness"
Philipp Schlicht (KGRC)
In joint results with Fabiana Castiblanco from 2018, we showed that
several classical tree forcings preserve sharps for reals and levels of
projective determinacy, and studied their impact on definable equivalence
relations (in particular, the question whether they add equivalence
classes to thin projective equivalence relations). I will discuss these
results and natural open problems on tree forcings and absoluteness that
arise from them.
Time and Place
This talk will be given via Zoom. If you haven't received the meeting link
by the day before the talk, please contact richard.springer@univie.ac.at!
Tagged: Philipp Schlicht
Barcelona Set Theory Seminar
Barcelona Logic Seminar
10/19/2020 9:21:05
Dear All,
Please find attached the announcement of the next session of the Barcelona Set Theory Seminar. Feel free to distribute it.
The Seminar will take place at the following address:
Best regards,
Joan
P.S.: If you do not wish to receive any more announcements, please send an email to
bagaria@ub.edu with the text “Unsubscribe”.
ICREA Research Professor
Universitat de Barcelona
Departament de Matemàtiques i Informàtica
Gran Via de les Corts Catalanes 585
08007 Barcelona
Catalonia
Phone: +34 93 402 1609
Barcelona Set Theory Seminar
Barcelona Logic Seminar
10/19/2020 9:21:23
Dear All,
Please find attached the announcement of the next session of the Barcelona Set Theory Seminar. Feel free to distribute it.
The Seminar will take place at the following address:
Best regards,
Joan
P.S.: If you do not wish to receive any more announcements, please send an email to
bagaria@ub.edu with the text “Unsubscribe”.
ICREA Research Professor
Universitat de Barcelona
Departament de Matemàtiques i Informàtica
Gran Via de les Corts Catalanes 585
08007 Barcelona
Catalonia
Phone: +34 93 402 1609
This Week in Logic at CUNY
This Week in Logic at CUNY
10/18/2020 22:15:53
This Week in Logic at CUNY:
- - - - Monday, Oct 19, 2020 - - - -
Logic and Metaphysics Workshop
Date: Monday, October 19th, 4.15-6.15 (NY time)
For meeting information, please email: yweiss@gradcenter.cuny.edu Michael Glanzberg (Rutgers)
Title: Models, Model Theory, and Modeling
Abstract: In this paper, I shall return to the relations between logic and semantics of natural language. My main goal is to advance a proposal about what that relation is. Logic as used in the study of natural language—an empirical discipline—functions much like specific kinds of scientific models. Particularly, I shall suggest, logics can function like analogical models. More provocatively, I shall also suggest they can function like model organisms often do in the biological sciences, providing a kind of controlled environment for observations. My focus here will be on a wide family of logics that are based on model theory, so in the end, these claims apply equally to model theory itself. Along the way towards arguing for my thesis about models in science, I shall also try to clarify the role of model theory in logic. At least, I shall suggest, it can play distinct roles in each domain. It can offer something like scientific models when it comes to empirical applications, while at the same time furthering conceptual analysis of a basic notion of logic.
- - - - Tuesday, Oct 20, 2020 - - - -
Computational Logic Seminar
Speakers: Pavel Naumov (King's College, Pennsylvania) and Rui-Jie Yew (Scripps College, California)
Title: An Epistemic Logic of Desire
Abstract: We say that an agent desires a condition phi if (1) the agent knows neither that phi is true nor that phi is false (2) among all indistinguishable worlds, she prefers those in which phi is true. In this talk, I will propose a sound and complete logical system that describes the interplay between the desire and the knowledge modalities in the multiagent setting.
- - - - Wednesday, Oct 21, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, Oct 21, 7:00pm
The seminar will take place virtually at 7pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Roman Kossak, CUNY
Types, gaps, and pairs of models of PA, Part III
The talk will be a survey of results on first-order theories of pairs (N,M), where M is a model of PA and N is its elementary extension, under various assumptions on the models and on the type of extension. In particular, I will discuss in detail the results on countable recursively saturated models and their cofinal submodels from a joint paper with Jim Schmerl.
The New York City Category Theory Seminar
Speaker: Andrei V. Rodin, Saint Petersburg State University.
Date and Time: Wednesday October 21, 2020, 7:00 - 8:30 PM., on Zoom.
- - - - Thursday, Oct 22, 2020 - - - -
- - - - Friday, Oct 23, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, Oct 23, 3pm
The seminar will take place virtually at 3pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. Gabriel Goldberg, University of Berkeley
Ultrapowers and the approximation property
Countably complete ultrafilters are the combinatorial manifestation of strong large cardinal axioms, but many of their basic properties are undecidable no matter the large cardinal axioms one is willing to adopt. The Ultrapower Axiom (UA) is a set theoretic principle that permits the development of a much clearer picture of countably complete ultrafilters and, consequently, the large cardinals from which they derive. It is not known whether UA is (relatively) consistent with very large cardinals, but assuming there is a canonical inner model with a supercompact cardinal, the answer should be yes: this inner model should satisfy UA and yet inherit all large cardinals present in the universe of sets. The predicted resemblance between the large cardinal structure of this model and that of the universe itself is so extreme as to suggest that certain consequences of UA must in fact be provable outright from large cardinal axioms. While the inner model theory of supercompact cardinals remains a major open problem, this talk will describe a technique that already permits a number of consequences of UA to be replicated from large cardinals alone. Still, the technique rests on the existence of inner models that absorb large cardinals, but instead of building canonical inner models, one takes ultrapowers.
Next Week in Logic at CUNY:
- - - - Monday, Oct 26, 2020 - - - -
- - - - Tuesday, Oct 27, 2020 - - - -
- - - - Wednesday, Oct 28, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, Oct 28, 2:00pm
The seminar will take place virtually at 2pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Victoria Gitman, CUNY
A model of second-order arithmetic satisfying AC but not DC
One of the strongest second-order arithmetic systems is full second-order arithmetic Z2Z2 which asserts that every second-order formula (with any number of set quantifiers) defines a set. We can augment Z2Z2 with choice principles such as the choice scheme and the dependent choice scheme. The Σ1nΣn1-choice scheme asserts for every Σ1nΣn1-formula φ(n,X)φ(n,X) that if for every nn, there is a set XX witnessing φ(n,X)φ(n,X), then there is a single set ZZ whose nn-th slice ZnZn is a witness for φ(n,X)φ(n,X). The Σ1nΣn1-dependent choice scheme asserts that every Σ1nΣn1-relation φ(X,Y)φ(X,Y) without terminal nodes has an infinite branch: there is a set ZZ such that φ(Zn,Zn+1)φ(Zn,Zn+1) holds for all nn. The system Z2Z2 proves the Σ12Σ21-choice scheme and the Σ12Σ21-dependent choice scheme. The independence of Π12Π21-choice scheme from Z2Z2 follows by taking a model of Z2Z2 whose sets are the reals of the Feferman-Levy model of ZFZF in which every ℵLnℵnL is countable and ℵLωℵωL is the first uncountable cardinal.
We construct a model of ZF+ACωZF+ACω whose reals give a model of Z2Z2 together with the full choice scheme in which Π12Π21-dependent choice fails. This result was first proved by Kanovei in 1979 and published in Russian. It was rediscovered by Sy Friedman and myself with a slightly simplified proof.
- - - - Thursday, Oct 29, 2020 - - - -
- - - - Friday, Oct 30, 2020 - - - -
- - - - Other Logic News - - - -
- - - - Web Site - - - -
Find us on the web at:
nylogic.github.io(site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to
jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email
jreitz@nylogic.org.
Logic Seminar 21 Oct 2020 17:00 hrs at NUS by Rupert Hoelzl (Universitaet der Bundeswehr Muenchen)
NUS Logic Seminar
10/15/2020 5:12:52
Invitation to the Logic Seminar at the National University of Singapore
Date: Wednesday, 21 Oct 2020, 17:00 hrs
Talk via Zoom:
https://nus-sg.zoom.us/j/96860201432?pwd=cVdwZmd2clVFaEhaTmJjaGdXMFdmdz09
Meeting ID: 968 6020 1432
Password: Is P=NP?
Speaker: Rupert Hoelzl, Universitaet der Bundeswehr Muenchen
Title: Monte Carlo Computability
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
We introduce Monte Carlo computability as a probabilistic concept of
computability on infinite objects and prove that Monte Carlo
computable functions are closed under composition. We then mutually
separate the following classes of functions from each other: the class
of multi-valued functions that are non-deterministically computable,
that of Las Vegas computable functions, and that of Monte Carlo
computable functions. We give natural examples of computational
problems witnessing these separations. As a specific problem
which is Monte Carlo computable but neither Las Vegas computable
nor non-deterministically computable, we study the problem of
sorting infinite sequences that was recently introduced by
Neumann and Pauly. Their results allow us to draw conclusions
about the relation between algebraic models and Monte Carlo computability.
Logic Seminar 28 Oct 2020 17:00 hrs at NUS by Liao Luke
NUS Logic Seminar
10/15/2020 5:00:58
Invitation to the Logic Seminar at the National University of Singapore
Date: Wednesday, 28 Oct 2020, 17:00 hrs
Talk via Zoom: https://nus-sg.zoom.us/j/96860201432?pwd=cVdwZmd2clVFaEhaTmJjaGdXMFdmdz09
Meeting ID: 968 6020 1432
Password: Is P=NP?
Speaker: Liao Luke
Title: Computability of Julia sets
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Abstract: TTE-computable is one of the major definitions of computable real
functions. We focus on a generalisation of TTE and check the basic
cases of computability of Julia sets. We prove quadratic polynomials
with Siegel disc incomputable in TTE is still incomputable in generalisation.
Logic Seminar 28 Oct 2020 17:00 hrs at NUS by Liao Yuke (typing errors corrected)
NUS Logic Seminar
10/15/2020 5:03:04
Invitation to the Logic Seminar at the National University of Singapore
Date: Wednesday, 28 Oct 2020, 17:00 hrs
Talk via Zoom: https://nus-sg.zoom.us/j/96860201432?pwd=cVdwZmd2clVFaEhaTmJjaGdXMFdmdz09
Meeting ID: 968 6020 1432
Password: Is P=NP?
Speaker: Liao Yuke
Title: Computability of Julia sets
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Abstract: TTE-computable is one of the major definitions of computable real
functions. We focus on a generalisation of TTE and check the basic
cases of computability of Julia sets. We prove quadratic polynomials
with Siegel disc incomputable in TTE is still incomputable in generalisation.
(KGRC) research seminar talk on Thursday, October 15
Kurt Godel Research Center
10/12/2020 11:19:04
The KGRC welcomes as guest:
Ziemowit Kostana (host: Noé de Rancourt) will visit from October 15 to October
20, 2020 and give a talk (see below).
* * *
Research seminar
Kurt Gödel Research Center
Thursday, October 15
"Fraïssé theory, and forcing absoluteness of rigidity for linear orders"
Ziemowit Kostana
(University of Warsaw, Poland)
During the talk I would like to introduce the theory of Cohen-like
first-order structures. These are countable or uncountable structures
which are "generic" much in the same sense as the Cohen reals. They can be
added to the universe of set theory using finite or, say, countable
conditions and exhibit different properties. I will focus on the
construction of a rigid linear order, whose rigidity is absolute for ccc
extensions.
Time and Place
This talk will be given via Zoom. If you haven't received the meeting link
by the day before the talk, please contact richard.springer@univie.ac.at!
This Week in Logic at CUNY
This Week in Logic at CUNY
10/11/2020 22:23:20
This Week in Logic at CUNY:
- - - - Monday, Oct 12, 2020 - - - -
Logic and Metaphysics Workshop
Date: Monday, October 12th, 4.15-6.15 (NY time)
For meeting information, please email: yweiss@gradcenter.cuny.edu Brian Cross Porter (CUNY).
Title: A Metainferential Hierachy of Validity Curry Paradoxes
Abstract: The validity curry paradox is a paradox involving a validity predicate which does not use any of the logical connectives; triviality can be derived using only the structural rules of Cut and Contraction with intuitively plausible rules for the validity predicate. This has been used to argue that we should move to a substructural logic dropping Cut or Contraction. In this talk, I’ll present metainferential versions of the validity curry paradox. We can recreate the validity curry paradox at the metainferential level, the metametainferential level, the metametametainferential level, and so on ad infinitum. I argue that this hierarchy of metaninferential validity curry paradoxes poses a problem for the standard substructural solutions to the validity curry paradox.
- - - - Tuesday, Oct 13, 2020 - - - -
Computational Logic Seminar
Speaker: Sergei Artemov, Graduate Center CUNY
Title: On aggregating probabilistic evidence
Abstract: Imagine a database—a set of propositions Γ = {F1, . . . , Fn} with some kind of probability estimates and let a proposition X logically follow from Γ . What is the best justified lower bound of the probability of X? The traditional approach, e.g. within Adams’ probability logic, computes the numeric lower bound for X corresponding to the worst-case scenario. We suggest a more flexible parameterized approach by assuming probability events u1, u2, . . . , un that support Γ and calculating aggregated evidence e(u1, u2, . . . , un) for X. The probability of e provides a tight lower bound for any, not only a worst-case, situation. The problem is formalized in a version of justification logic and the conclusions are supported by corresponding completeness theorems. This approach can handle conflicting and inconsistent data and allows the gathering both positive and negative evidence for the same proposition.
- - - - Wednesday, Oct 14, 2020 - - - -
The New York City Category Theory Seminar
Speaker: Jonathon Funk, Queensborough CUNY.
Date and Time: Wednesday October 14, 2020, 6:00 - 7:30PM (NOTICE DIFFERENT TIME) on Zoom.
For meeting zoom details email N. Yanofsky.Title: Pseudogroup Torsors.
Abstract: We use sheaf theory to analyze the topos of etale actions on the germ groupoid of a pseudogroup in the sense that we present a site for this topos, which we call the classifying topos of the pseudogroup. Our analysis carries us further into how pseudogroup morphisms and geometric morphisms are related. Ultimately, we shall see that the classifying topos classifies what we call a pseudogroup torsor. In hindsight, we see that pseudogroups form a bicategory of `flat' bimodules.
Joint work with Pieter Hofstra.
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, Oct 14, 7:00pm
The seminar will take place virtually at 7pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Roman Kossak, CUNY
Types, gaps, and pairs of models of PA, Part II
The talk will be a survey of results on first-order theories of pairs (N,M), where M is a model of PA and N is its elementary extension, under various assumptions on the models and on the type of extension. In particular, I will discuss in detail the results on countable recursively saturated models and their cofinal submodels from a joint paper with Jim Schmerl.
- - - - Thursday, Oct 15, 2020 - - - -
- - - - Friday, Oct 16, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, Oct 16, 3pm
The seminar will take place virtually at 3pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. Richard Matthews, University of Leeds
Taking Reinhardt's Power Away
Many large cardinals can be defined through elementary embeddings from the set-theoretic universe to some inner model, with the guiding principle being that the closer the inner model is to the universe the stronger the resulting theory. Under ZFC, the Kunen Inconsistency places a hard limit on how close this can be. One is then naturally led to the question of what theory is necessary to derive this inconsistency with the primary focus having historically been embeddings in ZF without Choice.
In this talk we take a different approach to weakening the required theory, which is to study elementary embeddings from the universe into itself in ZFC without Power Set. We shall see that I1, one of the largest large cardinal axioms not known to be inconsistent with ZFC, gives an upper bound to the naive version of this question. However, under reasonable assumptions, we can reobtain this inconsistency in our weaker theory.
Next Week in Logic at CUNY:
- - - - Monday, Oct 19, 2020 - - - -
Logic and Metaphysics Workshop
Date: Monday, October 19th, 4.15-6.15 (NY time)
For meeting information, please email: yweiss@gradcenter.cuny.edu Michael Glanzberg (Rutgers)
Title: Models, Model Theory, and Modeling
Abstract: In this paper, I shall return to the relations between logic and semantics of natural language. My main goal is to advance a proposal about what that relation is. Logic as used in the study of natural language—an empirical discipline—functions much like specific kinds of scientific models. Particularly, I shall suggest, logics can function like analogical models. More provocatively, I shall also suggest they can function like model organisms often do in the biological sciences, providing a kind of controlled environment for observations. My focus here will be on a wide family of logics that are based on model theory, so in the end, these claims apply equally to model theory itself. Along the way towards arguing for my thesis about models in science, I shall also try to clarify the role of model theory in logic. At least, I shall suggest, it can play distinct roles in each domain. It can offer something like scientific models when it comes to empirical applications, while at the same time furthering conceptual analysis of a basic notion of logic.
- - - - Tuesday, Oct 20, 2020 - - - -
- - - - Wednesday, Oct 21, 2020 - - - -
The New York City Category Theory Seminar
Speaker: Andrei V. Rodin, Saint Petersburg State University.
Date and Time: Wednesday October 21, 2020, 7:00 - 8:30 PM., on Zoom.
- - - - Thursday, Oct 22, 2020 - - - -
- - - - Friday, Oct 23, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, Oct 23, 3pm
The seminar will take place virtually at 3pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. Gabriel Goldberg, University of Berkeley
TBA
- - - - Other Logic News - - - -
- - - - Web Site - - - -
Find us on the web at:
nylogic.github.io(site designed, built & maintained by Victoria Gitman)
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Wednesday seminar
Prague Set Theory Seminar
10/11/2020 11:45:39
Dear all,
Well, no Wednesday seminar next week, no seminars until further notice.
Best,
David
Barcelona Set Theory Seminar
Barcelona Logic Seminar
10/11/2020 3:31:18
Dear All,
Please find attached the announcement of the next session of the Barcelona Set Theory Seminar. Feel free to distribute it.
The Seminar will take place at the following address:
Best regards,
Joan
P.S.: If you do not wish to receive any more announcements, please send an email to
bagaria@ub.edu with the text “Unsubscribe”.
Joan Bagaria
ICREA Research Professor
Universitat de Barcelona
Departament de Matemàtiques i Informàtica
Gran Via de les Corts Catalanes 585
08007 Barcelona
Catalonia
Phone: +34 93 402 1609
Logic Seminar 14 Oct 2020 17:00 hrs at NUS by Tran Chieu-Minh (University of Notre Dame)
NUS Logic Seminar
10/9/2020 1:12:36
Invitation to the Logic Seminar at the National University of Singapore
Date: Wednesday, 14 Oct 2020, 17:00 hrs
Talk via Zoom: https://nus-sg.zoom.us/j/96860201432?pwd=cVdwZmd2clVFaEhaTmJjaGdXMFdmdz09
Meeting ID: 968 6020 1432
Password: Is P=NP?
Speaker: Tran Chieu-Minh
Title: Incidence counting and trichotomy in o-minimal structures
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Abstract: Zarankiewicz's problem in graph theory asks to determine
the largest possible number of edges |E| in a bipartite graph G =
(V_1, V_2; E) with the parts V_1 and V_2 containing n_1 and n_2
vertices, respectively, and such that G contains no complete bipartite
subgraphs on k vertices. Graphs definable in o-minimal (or more
generally distal structures) enjoy stronger bounds than general
graphs, providing an abstract setting for the Szemeredi-Trotter
theorem and related incidence bounds. We obtain almost optimal upper
and lower bounds for hypergraphs definable in locally modular
o-minimal structures, along with some applications to incidence
counting (e.g. the number of incidences between points and boxes with
axis parallel sides on the plane whose incidence graph is K_{k,k}-free
is almost linear). We explain how the exponent appearing in these
bounds is tightly connected to the trichotomy principle in o-minimal
structures.
Joint work with Abdul Basit, Artem Chernikov, Sergei Starchenko and
Terence Tao.
Link to the Barcelona Set Theory Seminar
Barcelona Logic Seminar
10/6/2020 3:45:39
Dear All,
Just to let you know that the link to the Barcelona Set Theory Seminar is the following:
The first session of the Seminar will be tomorrow, Wednesday 7, at 16.00 (CEST). You may use the same link for all the following sessions.
See you there!
Joan
Joan Bagaria
ICREA Research Professor
Universitat de Barcelona
Departament de Matemàtiques i Informàtica
Gran Via de les Corts Catalanes 585
08007 Barcelona
Catalonia
Phone: +34 93 402 1609
Clovis Hamel: An introduction to Cp-theory and Grothendieck spaces
Toronto Set Theory Seminar
10/12/2021
Place: Fields Institute (Room 210)
Date: October 11, 2019 (13:30-15:00)
Speaker: Clovis Hamel
Title: An introduction to Cp-theory and Grothendieck spaces
Abstract: This is joint work with Prof. Frank Tall. An old theorem of Grothendieck states that countably compact subspaces of Cp(X) have compact closure whenever X is countably compact. We shall survey some basic results in Cp-theory and then focus on Grothendieck spaces, i.e. those for which the conclusion of Grothendieck theorem holds. Following Arhangel'skiĭ, we shall introduce the Lindelöf Σ-spaces, which belong to a wide class of well-behaved spaces, and prove that they are Grothendieck. We will show a compactness criterion for Fréchet-Urysohn Grothendieck spaces involving exchanging (ultra)limits which is similar to the classical Ptak's lemma. In a later occasion, we shall show the relevance of this results in Model Theory, e.g. the definability of pathological Banach spaces in various continuous logics.
Tagged: Clovis Hamel
(KGRC) research seminar talk on Thursday, October 8
Kurt Godel Research Center
10/5/2020 10:32:50
The KGRC welcomes as guests:
The visit by Jerzy Kąkol (host: Damian Sobota) had to be canceled due to
COVID travel restrictions.
The visit by Colin Jahel (host: Noé de Rancourt), too, had to be canceled
due to COVID travel restrictions; the talk will be given via Zoom (see
below).
Ziemowit Kostana (host: Noé de Rancourt) will visit from October 15 to
October 20, 2020 and give a talk (talk to be announced later).
* * *
Research seminar
Kurt Gödel Research Center
Thursday, October 8
"Actions of automorphism groups of Fraïssé limits on the space of linear
orderings"
Colin Jahel
(Claude Bernard University Lyon 1, France)
In 2005, Kechris, Pestov and Todorčević exhibited a correspondence between
combinatorial properties of structures and dynamical properties of their
automorphism groups. In 2012, Angel, Kechris and Lyons used this
correspondence to show the unique ergodicity of all the actions of some
groups. In this talk, I will give an overview of the aforementioned
results and discuss recent work generalizing results of Angel, Kechris and
Lyons.
Time and Place
Talk at 3:00pm
This talk will be given via Zoom. If you haven't received the meeting link
by the day before the talk, please contact richard.springer@univie.ac.at!
This Week in Logic at CUNY
This Week in Logic at CUNY
10/4/2020 21:34:47
This Week in Logic at CUNY:
- - - - Monday, Oct 5, 2020 - - - -
Logic and Metaphysics Workshop
Date: Monday, October 5th, 4.15-6.15 (NY time)
For meeting information, please email: yweiss@gradcenter.cuny.edu Speaker: Oliver Marshall (UNAM)
Title: Mathematical Information Content
Abstract: Alonzo Church formulated several logistic theories of propositions based on three alternative criteria of identity (1949, 1954, 1989, 1993). The most coarse grained of these criteria is Alternative (2), according to which two propositions are identical iff the sentences that express them are necessarily materially equivalent. Alternative (1) is more discerning. According to Alternative (1), two propositions are identical iff the sentences that express them can be obtained from one another by the substitution of synonyms for synonyms and λ-conversion. Church said that he intended this to limn a notion of proposition closely related to Frege’s notion of gedanke, but added that it will not be sufficiently discerning if propositions in the sense of Alternative (1) are taken as objects of assertion and belief (1993). Alternative (0), the most discerning criterion, says that two propositions are identical iff the sentences that express them can be obtained from one another by the substitution of synonyms for synonyms. I argue that Alternative (1) does indeed provide insight into one of the topics that concerned Frege (1884) – namely, abstraction. Then I discuss various counterexamples to Church’s criteria (including one due to Paul Bernays, 1961). I close by proposing a criterion of identity for mathematical information content based on the various examples under discussion.
- - - - Tuesday, Oct 6, 2020 - - - -
Computational Logic Seminar
Tuesday, Oct 6, 2-4pm
Speaker: John Connor, Graduate Center CUNY
Title: Justification Logics as Internal Languages -- Part 1 of 2
Abstract:
This is the first of two talks in which I answer the question (in the affirmative) of whether the justification logic J is the internal language of a class of categories. In this first talk we will discuss the methods by which a logic may be interpreted in a category, and the properties such interpretations may have. Concrete examples will include propositional intuitionistic logic as the internal language of bi-Cartesian closed categories. Some aspects of the interpretation of higher logics in topoi will also be discussed. Previous knowledge of category theory is not assumed.
The talk concludes with a discussion of the difficulties inherent in the interpretation of justification logics. In the next talk, a class of categories is presented with respect to which the justification logic J is sound and complete in a weak sense.
- - - - Wednesday, Oct 7, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, Oct 7, 7:00pm
The seminar will take place virtually at 7pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Roman Kossak, CUNY
Types, gaps, and pairs of models of PA
- - - - Thursday, Oct 8, 2020 - - - -
- - - - Friday, Oct 9, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, Oct 9, 11am
The seminar will take place virtually at 11am US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. Heike Mildenberger, Albert-Ludwigs-Universität Freiburg
Forcing with variants of Miller trees
Guzmán and Kalajdzievski introduced a variant of Miller forcing P(F)P(F) that diagonalises a given filter FF over ωω and has Axiom A. We investigate the effect of P(F)P(F) for particularly chosen Canjar filters FF. This is joint work with Christian Bräuninger.
Next Week in Logic at CUNY:
- - - - Monday, Oct 12, 2020 - - - -
Logic and Metaphysics Workshop
Date: Monday, October 12th, 4.15-6.15 (NY time)
For meeting information, please email: yweiss@gradcenter.cuny.edu Brian Cross Porter (CUNY).
Title: A Metainferential Hierachy of Validity Curry Paradoxes
Abstract: The validity curry paradox is a paradox involving a validity predicate which does not use any of the logical connectives; triviality can be derived using only the structural rules of Cut and Contraction with intuitively plausible rules for the validity predicate. This has been used to argue that we should move to a substructural logic dropping Cut or Contraction. In this talk, I’ll present metainferential versions of the validity curry paradox. We can recreate the validity curry paradox at the metainferential level, the metametainferential level, the metametametainferential level, and so on ad infinitum. I argue that this hierarchy of metaninferential validity curry paradoxes poses a problem for the standard substructural solutions to the validity curry paradox.
- - - - Tuesday, Oct 13, 2020 - - - -
- - - - Wednesday, Oct 14, 2020 - - - -
The New York City Category Theory Seminar
Speaker: Jonathon Funk, Queensborough CUNY.
Date and Time: Wednesday October 14, 2020, 6:00 - 7:30PM (NOTICE DIFFERENT TIME) on Zoom.
For meeting zoom details email N. Yanofsky.Title: Pseudogroup Torsors.
Abstract: We use sheaf theory to analyze the topos of etale actions on the germ groupoid of a pseudogroup in the sense that we present a site for this topos, which we call the classifying topos of the pseudogroup. Our analysis carries us further into how pseudogroup morphisms and geometric morphisms are related. Ultimately, we shall see that the classifying topos classifies what we call a pseudogroup torsor. In hindsight, we see that pseudogroups form a bicategory of `flat' bimodules.
Joint work with Pieter Hofstra.
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, Oct 14, 7:00pm
The seminar will take place virtually at 7pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Roman Kossak, CUNY
Types, gaps, and pairs of models of PA
- - - - Thursday, Oct 15, 2020 - - - -
- - - - Friday, Oct 16, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, Oct 16, 3pm
The seminar will take place virtually at 3pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. Richard Matthews, University of Leeds
TBA
- - - - Other Logic News - - - -
Ad hoc logic workshop
There is some interesting work going on in NYC at the moment on substructural logics, hierarchies thereof, and solutions to the liar. So we're scheduling an ad hoc workshop on these matters (by Zoom), with talks by Mel Fitting, Will Nava, Brian Porter, and Chris Scambler. It will be on Friday 30th October. The aim will be to have two papers in the morning, and two in the afternoon. Full details will be sent round in due course. This is just an early warning to make a note of the date if you are interested. - Graham Priest
- - - - Web Site - - - -
Find us on the web at:
nylogic.github.io(site designed, built & maintained by Victoria Gitman)
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Wednesday seminar
Prague Set Theory Seminar
10/4/2020 15:52:49
Dear all,
Still no seminar the coming Wednesday, October 7th.
Unless there is a major the development, I expect the seminar to resume
on Wednesday October 14th. (The originally scheduled off-site meeting
got cancelled.)
Best,
David
Invitation to Logic Seminar 7 Oct 2020 17:00 hrs at NUS by Wu Guohua
NUS Logic Seminar
10/2/2020 9:28:07
Invitation to the Logic Seminar at the National University of Singapore
Date: Wednesday, 7 October 2020, 17:00 hrs
Talk via Zoom: https://nus-sg.zoom.us/j/96860201432?pwd=cVdwZmd2clVFaEhaTmJjaGdXMFdmdz09
Meeting ID: 968 6020 1432
Password: Is P=NP?
Speaker: Wu Guohua
Title: Splittings
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Abstract: I will present a survey of splittings in sets and in
degrees. Downey-Stob's long paper in 1993 provides a comprehensive and
updated survey. In this talk, I first recall some classical theorems
on this topic, both ideas and techniques, and following this, I will
present some results along this line being done in the last few years.
Tagged: Wu Guohua
Barcelona Set Theory seminar
Barcelona Set Theory Seminar
10/1/2020 10:59:55
Dear Colleague,
Next week we will start our online Barcelona Set Theory seminar, which will meet every Wednesday at 4:00 (CEST). Please find attached the announcement of the next session. Feel free to distribute it.
If you wish to attend, please send an email to
bagaria@ub.edu and we’ll send you the link.
Best regards,
Joan
Joan Bagaria
ICREA Research Professor
Universitat de Barcelona
Departament de Matemàtiques i Informàtica
Gran Via de les Corts Catalanes 585
08007 Barcelona
Catalonia
Phone: +34 93 402 1609
This Week in Logic at CUNY
This Week in Logic at CUNY
9/27/2020 21:59:56
This Week in Logic at CUNY:
- - - - Monday, Sep 21, 2020 - - - -
Logic and Metaphysics Workshop
Date: Monday, September 21st, 4.15-6.15 (NY time)
For zoom information, email Yale Weiss at: yweiss@gradcenter.cuny.edu.
Speaker: Yale Weiss (CUNY)
Title: Arithmetical Semantics for Non-Classical Logic
Abstract: I consider logics which can be characterized exactly in the lattice of the positive integers ordered by division. I show that various (fragments of) relevant logics and intuitionistic logic are sound and complete with respect to this structure taken as a frame; different logics are characterized in it by imposing different conditions on valuations. This presentation will both cover and extend previous/forthcoming work of mine on the subject.
- - - - Tuesday, Sep 22, 2020 - - - -
Computational Logic Seminar
Time 2:00 - 4:00 PM Tuesday, September 22, 2020
Please send me a request for a link to this talk: (unless you are registered or have already sent me a request for the whole semester).
Speaker: Hirohiko Kushida, Graduate Center, City University of New York
Title: Reduction of Modal Logic and Realization in Justification Logic
Abstract: In this paper, we first offer basic results on modal logic: (1) a wide range of modal systems can be syntactically reduced to the modal logic K in terms of theoremhood and (2) we can restrict the forms of modal axioms without changing their deductive power in those range of modal logics. Then, based on these results, we offer a new, simple, uniform and modular proof-theoretical proof of the realization of a wide range of modal logics with possible combinations of modal axioms T, D, 4, 5 including S5 in Justification Logic. We do not use a generalization of sequent calculus such as hypersequent and nested sequent calculi. We just utilize the standard cut-free sequent calculus for K and then we show, in the realized proof in Justification Logic (corresponding to K), how to recover the realizations of the modal axioms by rewriting terms in the proof.
- - - - Wednesday, Sep 23, 2020 - - - -
- - - - Thursday, Sep 24, 2020 - - - -
Seminar in Philosophical Logic
Thursday, Sep 24, 6:30 PM.
(Zoom link upon request
RParikh@gc.cuny.edu; will be sent automatically to seminar members)
Arthur Paul Pedersen, Department of Computer Science, City College of New York, CUNY
Coherent Judgment: Previsions and Forecasts
Abstract. This talk is to continue critical discussion of Persi Diaconis and Brian Skyrms' book chapter, "Judgment," from their Ten Great Ideas about Chance (Princeton University Press, 2018). Specifically, I will cover two variations on coherence advanced by de Finetti to justify his theory of personal probability, each cast in game-theoretic terms — one based on previsions, the other based on forecasting. I will show how his ideas extend both conceptually and mathematically to subsequent developments due to Savage, Anscombe & Aumann, and others. While the talk is to be self-contained, an excellent reference for broader discussion is Peter Fishburn's "Utility and Subjective Probability: Contemporary Theories," International Encyclopedia of the Social & Behavioral Sciences, 2001: 16113-16121.
- - - - Friday, Sep 25, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, Sep 25, 11am
The seminar will take place virtually at 11am US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. Ralf Schindler, University of MünsterMartin's Maximum^++ implies the P_max axiom (*)
Forcing axioms spell out the dictum that if a statement can be forced, then it is already true. The P_max axiom (*) goes beyond that by claiming that if a statement is consistent, then it is already true. Here, the statement in question needs to come from a resticted class of statements, and 'consistent' needs to mean 'consistent in a strong sense.' It turns out that (*) is actually equivalent to a forcing axiom, and the proof is by showing that the (strong) consistency of certain theories gives rise to a corresponding notion of forcing producing a model of that theory. This is joint work with D. Asperó building upon earlier work of R. Jensen and (ultimately) Keisler's 'consistency properties'.
Next Week in Logic at CUNY:
- - - - Monday, Sep 28, 2020 - - - -
Logic and Metaphysics Workshop
Date: Monday, September 29st, 4.15-6.15 (NY time)
For zoom information, email Yale Weiss at: yweiss@gradcenter.cuny.edu.
Speaker: Daniel Hoek (Virginia Tech)
Title: Coin flips, Spinning Tops and the Continuum Hypothesis
Abstract: By using a roulette wheel or by flipping a countable infinity of fair coins, we can randomly pick out a point on a continuum. In this talk I will show how to combine this simple observation with general facts about chance to investigate the cardinality of the continuum. In particular I will argue on this basis that the continuum hypothesis is false. More specifically, I argue that the probabilistic inductive methods standardly used in science presuppose that every proposition about the outcome of a chancy process has a certain chance between 0 and 1. I also argue in favour of the standard view that chances are countably additive. A classic theorem from Banach and Kuratowski (1929), tells us that it follows, given the axioms of ZFC, that there are cardinalities between countable infinity and the cardinality of the continuum. (Get the paper here:
https://philpapers.org/archive/HOECAT-2.pdf).
- - - - Tuesday, Sep 29, 2020 - - - -
- - - - Wednesday, Sep 30, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, Sep 30, 2:00pm
The seminar will take place virtually at 2pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Leszek Kołodziejczyk University of Warsaw
Ramsey's Theorem over RCA∗0RCA0∗: Part II
Abstract: The usual base theory used in reverse mathematics, RCA0RCA0, is the fragment of second-order arithmetic axiomatized by Δ01Δ10 comprehension and Σ01Σ10 induction. The weaker base theory RCA∗0RCA0∗ is obtained by replacing Σ01Σ10 induction with Δ01Δ10 induction (and adding the well-known axiom expexp in order to ensure totality of the exponential function). In first-order terms, RCA0RCA0 is conservative over IΣ1IΣ1 and RCA∗0RCA0∗ is conservative over BΣ1+expBΣ1+exp.
Some of the most interesting open problems in reverse mathematics concern the first-order strength of statements from Ramsey Theory, in particular Ramsey's Theorem for pairs and two colours. In this talk, I will discuss joint work with Kasia Kowalik, Tin Lok Wong, and Keita Yokoyama concerning the strength of Ramsey's Theorem over RCA∗0RCA0∗.
Given standard natural numbers
n,k≥2n,k≥2, let
RTnkRTkn stand for Ramsey's Theorem for
kk-colourings of
nn-tuples. We first show that assuming the failure of
Σ01Σ10 induction,
RTnkRTkn is equivalent to its own relativization to an arbitrary
Σ01Σ10-definable cut. Using this, we give a complete axiomatization of the first-order consequences of
RCA∗0+RTnkRCA0∗+RTkn for
n≥3n≥3 (this turns out to be a rather peculiar fragment of PA) and obtain some nontrivial information about the first-order consequences of
RT2kRTk2. Time permitting, we will also discuss the question whether our results have any relevance for the well-known open problem of characterizing the first-order consequences of
RT22RT22 over the traditional base theory
RCA0RCA0.
In the first part of the talk, we concentrated on Ramsey's Theorem for nn-tuples where n≥3n≥3. In this second part, the focus will be on RT22RT22.
The New York City Category Theory Seminar
Date and Time: Wednesday September 30, 2020, 7:00 - 8:30 PM., on Zoom.
Zoom information will be posted on the web page on the day of the talk http://www.sci.brooklyn.cuny.edu/~noson/CTseminar.htmlSpeaker: David Ellerman, University of Ljubljana.
Title: The Logical Theory of Canonical Maps: The Elements & Distinctions Analysis of the Morphisms, Duality, Canonicity, and Universal Constructions in Sets.
Abstract: Category theory gives a mathematical characterization of naturality but not of canonicity. The purpose of this paper is to develop the logical theory of canonical maps based on the broader demonstration that the dual notions of elements & distinctions are the basic analytical concepts needed to unpack and analyze morphisms, duality, canonicity, and universal constructions in Sets, the category of sets and functions. The analysis extends directly to other Sets-based concrete categories (groups, rings, vector spaces, etc.). Elements and distinctions are the building blocks of the two dual logics, the Boolean logic of subsets and the logic of partitions. The partial orders (inclusion and refinement) in the lattices for the dual logics define morphisms. The thesis is that the maps that are canonical in Sets are the ones that are defined (given the data of the situation) by these two logical partial orders and by the compositions of those maps.
Paper: Available here
http://www.sci.brooklyn.cuny.edu/~noson/Ellerman2020.pdf
- - - - Thursday, Oct 1, 2020 - - - -
- - - - Friday, Oct 2, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, Oct 2, 11am
The seminar will take place virtually at 11am US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. David Aspero, University of East Anglia
Martin’s Maximum^++ implies the P_max axiom (*) (Part 2)
This will be a sequel to Ralf Schindler’s talk on 9/25. My plan is to give a reasonably detailed account of the proof of the result in the title.
Next Week in Logic at CUNY:
- - - - Monday, Oct 5, 2020 - - - -
- - - - Tuesday, Oct 6, 2020 - - - -
- - - - Wednesday, Oct 7, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, Oct 7, 7:00pm
The seminar will take place virtually at 7pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Roman Kossak, CUNY
Types, gaps, and pairs of models of PA
- - - - Thursday, Oct 8, 2020 - - - -
- - - - Friday, Oct 9, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, Oct 9, 11am
The seminar will take place virtually at 11am US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. Heike Mildenberger, Albert-Ludwigs-Universität Freiburg
TBA
- - - - Other Logic News - - - -
Ad hoc logic workshop
There is some interesting work going on in NYC at the moment on substructural logics, hierarchies thereof, and solutions to the liar. So we're scheduling an ad hoc workshop on these matters (by Zoom), with talks by Mel Fitting, Will Nava, Brian Porter, and Chris Scambler. It will be on Friday 30th October. The aim will be to have two papers in the morning, and two in the afternoon. Full details will be sent round in due course. This is just an early warning to make a note of the date if you are interested. - Graham Priest
- - - - Web Site - - - -
Find us on the web at:
nylogic.github.io(site designed, built & maintained by Victoria Gitman)
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Wednesday seminar
Prague Set Theory Seminar
9/27/2020 8:14:24
Dear all,
As the general epidemiological situation remains uncertain, there will
be no seminar next week, Wednesday October 30th.
I expect the seminar to resume during October. (Probably no seminar on
October 14th -- our Institute holds an off-site meeting.)
Best,
David
Logic Seminar 30 Sept 2020 17:00 hrs by Vasco Brattka (Universitaet der Bundeswehr Muenchen)
NUS Logic Seminar
9/23/2020 23:49:10
Invitation to the Logic Seminar at the National University of Singapore
Date: Wednesday, 30 September 2020, 17:00 hrs
Talk via Zoom: https://nus-sg.zoom.us/j/96860201432?pwd=cVdwZmd2clVFaEhaTmJjaGdXMFdmdz09
Meeting ID: 968 6020 1432
Password: Is P=NP?
Speaker: Vasco Brattka
Title: The Discontinuity Problem
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Abstract
We discuss the question whether there is a weakest unsolvable
mathematical problem. In recent years the Weihrauch lattice has
been established as a suitable computability theoretic framework
to analyze the uniform computational content of problems from many
different fields of mathematics. Here we answer a question by
Schroeder, whether there is a weakest discontinuous problem with
respect to the continuous version of Weihrauch reducibility.
We introduce the discontinuity problem, and we show that it
is reducible exactly to the effectively discontinuous problems,
defined in a suitable way. However, in which sense this answers
Schroeder's question sensitively depends on the axiomatic framework
that is chosen and it is a positive answer if we work in Zermelo-
Fraenkel set theory with dependent choice and the axiom of determinacy.
On the other hand, using the axiom of choice, one can construct
problems which are discontinuous, but not effectively so.
Hence, the exact structure of the ``bottom'' of the Weihrauch lattice
sensitively depends on the axiomatic setting that we choose.
We prove our result using Wadge games for mathematical problems and
while the existence of a winning strategy for player II characterizes
continuity of the problem (as already shown by Nobrega and Pauly),
the existence of a winning strategy for player I characterizes
effective discontinuity of the problem. We also provide further
insights into the algebraic nature of the discontinuity problem.
For one we show that the parallelization of the discontinuity
problem is exactly the non-computability problem that was studied
before. One the other hand, we introduce a new algebraic operation
in the Weihrauch lattice that we call summation and which is the
dual operation to parallelization. While parallelization can be
seen as an analogue of the bang operator in linear logic, summation
can be seen as an analogue of the question mark operator.
It turns out that the discontinuity problem can be obtained as
summation of a number of well-known problems in the Weihrauch
lattice, such as the (lesser) limited problem of omniscience
and variants thereof. More generally, we study the action of
the monoid formed by parallelization and summation on the
Weihrauch lattice, and we prove that this action can lead to
at most five different Weihrauch degrees, which (in the maximal case)
are always organized in a pentagon. We show that the discontinuity
problem appears as the bottom of several natural such pentagons.
This leads to further interesting characterizations of the
discontinuity problem.
Tagged: Vasco Brattka
UPDATE - This Week in Logic at CUNY
This Week in Logic at CUNY
9/20/2020 22:00:19
Added the talk on Tuesday Sep 22 in the Computational Logic Seminar
-Jonas
This Week in Logic at CUNY:
- - - - Monday, Sep 21, 2020 - - - -
Logic and Metaphysics Workshop
Date: Monday, September 21st, 4.15-6.15 (NY time)
For zoom information, email Yale Weiss at: yweiss@gradcenter.cuny.edu.
Speaker: Yale Weiss (CUNY)
Title: Arithmetical Semantics for Non-Classical Logic
Abstract: I consider logics which can be characterized exactly in the lattice of the positive integers ordered by division. I show that various (fragments of) relevant logics and intuitionistic logic are sound and complete with respect to this structure taken as a frame; different logics are characterized in it by imposing different conditions on valuations. This presentation will both cover and extend previous/forthcoming work of mine on the subject.
- - - - Tuesday, Sep 22, 2020 - - - -
Computational Logic Seminar
Time 2:00 - 4:00 PM Tuesday, September 22, 2020
Please send me a request for a link to this talk: (unless you are registered or have already sent me a request for the whole semester).
Speaker: Hirohiko Kushida, Graduate Center, City University of New York
Title: Reduction of Modal Logic and Realization in Justification Logic
Abstract: In this paper, we first offer basic results on modal logic: (1) a wide range of modal systems can be syntactically reduced to the modal logic K in terms of theoremhood and (2) we can restrict the forms of modal axioms without changing their deductive power in those range of modal logics. Then, based on these results, we offer a new, simple, uniform and modular proof-theoretical proof of the realization of a wide range of modal logics with possible combinations of modal axioms T, D, 4, 5 including S5 in Justification Logic. We do not use a generalization of sequent calculus such as hypersequent and nested sequent calculi. We just utilize the standard cut-free sequent calculus for K and then we show, in the realized proof in Justification Logic (corresponding to K), how to recover the realizations of the modal axioms by rewriting terms in the proof.
- - - - Wednesday, Sep 23, 2020 - - - -
- - - - Thursday, Sep 24, 2020 - - - -
Seminar in Philosophical Logic
Thursday, Sep 24, 6:30 PM.
(Zoom link upon request
RParikh@gc.cuny.edu; will be sent automatically to seminar members)
Arthur Paul Pedersen, Department of Computer Science, City College of New York, CUNY
Coherent Judgment: Previsions and Forecasts
Abstract. This talk is to continue critical discussion of Persi Diaconis and Brian Skyrms' book chapter, "Judgment," from their Ten Great Ideas about Chance (Princeton University Press, 2018). Specifically, I will cover two variations on coherence advanced by de Finetti to justify his theory of personal probability, each cast in game-theoretic terms — one based on previsions, the other based on forecasting. I will show how his ideas extend both conceptually and mathematically to subsequent developments due to Savage, Anscombe & Aumann, and others. While the talk is to be self-contained, an excellent reference for broader discussion is Peter Fishburn's "Utility and Subjective Probability: Contemporary Theories," International Encyclopedia of the Social & Behavioral Sciences, 2001: 16113-16121.
- - - - Friday, Sep 25, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, Sep 25, 11am
The seminar will take place virtually at 11am US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. Ralf Schindler, University of MünsterMartin's Maximum^++ implies the P_max axiom (*)
Forcing axioms spell out the dictum that if a statement can be forced, then it is already true. The P_max axiom (*) goes beyond that by claiming that if a statement is consistent, then it is already true. Here, the statement in question needs to come from a resticted class of statements, and 'consistent' needs to mean 'consistent in a strong sense.' It turns out that (*) is actually equivalent to a forcing axiom, and the proof is by showing that the (strong) consistency of certain theories gives rise to a corresponding notion of forcing producing a model of that theory. This is joint work with D. Asperó building upon earlier work of R. Jensen and (ultimately) Keisler's 'consistency properties'.
Next Week in Logic at CUNY:
- - - - Monday, Sep 28, 2020 - - - -
Logic and Metaphysics Workshop
Date: Monday, September 29st, 4.15-6.15 (NY time)
For zoom information, email Yale Weiss at: yweiss@gradcenter.cuny.edu.
Speaker: Daniel Hoek (Virginia Tech)
Title: Coin flips, Spinning Tops and the Continuum Hypothesis
Abstract: By using a roulette wheel or by flipping a countable infinity of fair coins, we can randomly pick out a point on a continuum. In this talk I will show how to combine this simple observation with general facts about chance to investigate the cardinality of the continuum. In particular I will argue on this basis that the continuum hypothesis is false. More specifically, I argue that the probabilistic inductive methods standardly used in science presuppose that every proposition about the outcome of a chancy process has a certain chance between 0 and 1. I also argue in favour of the standard view that chances are countably additive. A classic theorem from Banach and Kuratowski (1929), tells us that it follows, given the axioms of ZFC, that there are cardinalities between countable infinity and the cardinality of the continuum. (Get the paper here:
https://philpapers.org/archive/HOECAT-2.pdf).
- - - - Tuesday, Sep 29, 2020 - - - -
- - - - Wednesday, Sep 30, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, Sep 30, 2:00pm
The seminar will take place virtually at 2pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Leszek Kołodziejczyk University of Warsaw
Ramsey's Theorem over RCA∗0RCA0∗: Part II
Abstract: The usual base theory used in reverse mathematics, RCA0RCA0, is the fragment of second-order arithmetic axiomatized by Δ01Δ10 comprehension and Σ01Σ10 induction. The weaker base theory RCA∗0RCA0∗ is obtained by replacing Σ01Σ10 induction with Δ01Δ10 induction (and adding the well-known axiom expexp in order to ensure totality of the exponential function). In first-order terms, RCA0RCA0 is conservative over IΣ1IΣ1 and RCA∗0RCA0∗ is conservative over BΣ1+expBΣ1+exp.
Some of the most interesting open problems in reverse mathematics concern the first-order strength of statements from Ramsey Theory, in particular Ramsey's Theorem for pairs and two colours. In this talk, I will discuss joint work with Kasia Kowalik, Tin Lok Wong, and Keita Yokoyama concerning the strength of Ramsey's Theorem over RCA∗0RCA0∗.
Given standard natural numbers
n,k≥2n,k≥2, let
RTnkRTkn stand for Ramsey's Theorem for
kk-colourings of
nn-tuples. We first show that assuming the failure of
Σ01Σ10 induction,
RTnkRTkn is equivalent to its own relativization to an arbitrary
Σ01Σ10-definable cut. Using this, we give a complete axiomatization of the first-order consequences of
RCA∗0+RTnkRCA0∗+RTkn for
n≥3n≥3 (this turns out to be a rather peculiar fragment of PA) and obtain some nontrivial information about the first-order consequences of
RT2kRTk2. Time permitting, we will also discuss the question whether our results have any relevance for the well-known open problem of characterizing the first-order consequences of
RT22RT22 over the traditional base theory
RCA0RCA0.
In the first part of the talk, we concentrated on Ramsey's Theorem for nn-tuples where n≥3n≥3. In this second part, the focus will be on RT22RT22.
The New York City Category Theory Seminar
Date and Time: Wednesday September 30, 2020, 7:00 - 8:30 PM., on Zoom.
Zoom information will be posted on the web page on the day of the talk http://www.sci.brooklyn.cuny.edu/~noson/CTseminar.htmlSpeaker: David Ellerman, University of Ljubljana.
Title: The Logical Theory of Canonical Maps: The Elements & Distinctions Analysis of the Morphisms, Duality, Canonicity, and Universal Constructions in Sets.
Abstract: Category theory gives a mathematical characterization of naturality but not of canonicity. The purpose of this paper is to develop the logical theory of canonical maps based on the broader demonstration that the dual notions of elements & distinctions are the basic analytical concepts needed to unpack and analyze morphisms, duality, canonicity, and universal constructions in Sets, the category of sets and functions. The analysis extends directly to other Sets-based concrete categories (groups, rings, vector spaces, etc.). Elements and distinctions are the building blocks of the two dual logics, the Boolean logic of subsets and the logic of partitions. The partial orders (inclusion and refinement) in the lattices for the dual logics define morphisms. The thesis is that the maps that are canonical in Sets are the ones that are defined (given the data of the situation) by these two logical partial orders and by the compositions of those maps.
Paper: Available here
http://www.sci.brooklyn.cuny.edu/~noson/Ellerman2020.pdf
- - - - Thursday, Oct 1, 2020 - - - -
- - - - Friday, Oct 2, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, Oct 2, 3pm
The seminar will take place virtually at 3pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. David Aspero, University of East Anglia
TBA
- - - - Other Logic News - - - -
- - - - Web Site - - - -
Find us on the web at:
nylogic.github.io(site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to
jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email
jreitz@nylogic.org.
This Week in Logic at CUNY
This Week in Logic at CUNY
9/20/2020 21:54:11
This Week in Logic at CUNY:
- - - - Monday, Sep 21, 2020 - - - -
Logic and Metaphysics Workshop
Date: Monday, September 21st, 4.15-6.15 (NY time)
For zoom information, email Yale Weiss at: yweiss@gradcenter.cuny.edu.
Speaker: Yale Weiss (CUNY)
Title: Arithmetical Semantics for Non-Classical Logic
Abstract: I consider logics which can be characterized exactly in the lattice of the positive integers ordered by division. I show that various (fragments of) relevant logics and intuitionistic logic are sound and complete with respect to this structure taken as a frame; different logics are characterized in it by imposing different conditions on valuations. This presentation will both cover and extend previous/forthcoming work of mine on the subject.
- - - - Tuesday, Sep 22, 2020 - - - -
- - - - Wednesday, Sep 23, 2020 - - - -
- - - - Thursday, Sep 24, 2020 - - - -
Seminar in Philosophical Logic
Thursday, Sep 24, 6:30 PM.
(Zoom link upon request
RParikh@gc.cuny.edu; will be sent automatically to seminar members)
Arthur Paul Pedersen, Department of Computer Science, City College of New York, CUNY
Coherent Judgment: Previsions and Forecasts
Abstract. This talk is to continue critical discussion of Persi Diaconis and Brian Skyrms' book chapter, "Judgment," from their Ten Great Ideas about Chance (Princeton University Press, 2018). Specifically, I will cover two variations on coherence advanced by de Finetti to justify his theory of personal probability, each cast in game-theoretic terms — one based on previsions, the other based on forecasting. I will show how his ideas extend both conceptually and mathematically to subsequent developments due to Savage, Anscombe & Aumann, and others. While the talk is to be self-contained, an excellent reference for broader discussion is Peter Fishburn's "Utility and Subjective Probability: Contemporary Theories," International Encyclopedia of the Social & Behavioral Sciences, 2001: 16113-16121.
- - - - Friday, Sep 25, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, Sep 25, 11am
The seminar will take place virtually at 11am US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. Ralf Schindler, University of MünsterMartin's Maximum^++ implies the P_max axiom (*)
Forcing axioms spell out the dictum that if a statement can be forced, then it is already true. The P_max axiom (*) goes beyond that by claiming that if a statement is consistent, then it is already true. Here, the statement in question needs to come from a resticted class of statements, and 'consistent' needs to mean 'consistent in a strong sense.' It turns out that (*) is actually equivalent to a forcing axiom, and the proof is by showing that the (strong) consistency of certain theories gives rise to a corresponding notion of forcing producing a model of that theory. This is joint work with D. Asperó building upon earlier work of R. Jensen and (ultimately) Keisler's 'consistency properties'.
Next Week in Logic at CUNY:
- - - - Monday, Sep 28, 2020 - - - -
Logic and Metaphysics Workshop
Date: Monday, September 29st, 4.15-6.15 (NY time)
For zoom information, email Yale Weiss at: yweiss@gradcenter.cuny.edu.
Speaker: Daniel Hoek (Virginia Tech)
Title: Coin flips, Spinning Tops and the Continuum Hypothesis
Abstract: By using a roulette wheel or by flipping a countable infinity of fair coins, we can randomly pick out a point on a continuum. In this talk I will show how to combine this simple observation with general facts about chance to investigate the cardinality of the continuum. In particular I will argue on this basis that the continuum hypothesis is false. More specifically, I argue that the probabilistic inductive methods standardly used in science presuppose that every proposition about the outcome of a chancy process has a certain chance between 0 and 1. I also argue in favour of the standard view that chances are countably additive. A classic theorem from Banach and Kuratowski (1929), tells us that it follows, given the axioms of ZFC, that there are cardinalities between countable infinity and the cardinality of the continuum. (Get the paper here:
https://philpapers.org/archive/HOECAT-2.pdf).
- - - - Tuesday, Sep 29, 2020 - - - -
- - - - Wednesday, Sep 30, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, Sep 30, 2:00pm
The seminar will take place virtually at 2pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Leszek Kołodziejczyk University of Warsaw
Ramsey's Theorem over RCA∗0RCA0∗: Part II
Abstract: The usual base theory used in reverse mathematics, RCA0RCA0, is the fragment of second-order arithmetic axiomatized by Δ01Δ10 comprehension and Σ01Σ10 induction. The weaker base theory RCA∗0RCA0∗ is obtained by replacing Σ01Σ10 induction with Δ01Δ10 induction (and adding the well-known axiom expexp in order to ensure totality of the exponential function). In first-order terms, RCA0RCA0 is conservative over IΣ1IΣ1 and RCA∗0RCA0∗ is conservative over BΣ1+expBΣ1+exp.
Some of the most interesting open problems in reverse mathematics concern the first-order strength of statements from Ramsey Theory, in particular Ramsey's Theorem for pairs and two colours. In this talk, I will discuss joint work with Kasia Kowalik, Tin Lok Wong, and Keita Yokoyama concerning the strength of Ramsey's Theorem over RCA∗0RCA0∗.
Given standard natural numbers
n,k≥2n,k≥2, let
RTnkRTkn stand for Ramsey's Theorem for
kk-colourings of
nn-tuples. We first show that assuming the failure of
Σ01Σ10 induction,
RTnkRTkn is equivalent to its own relativization to an arbitrary
Σ01Σ10-definable cut. Using this, we give a complete axiomatization of the first-order consequences of
RCA∗0+RTnkRCA0∗+RTkn for
n≥3n≥3 (this turns out to be a rather peculiar fragment of PA) and obtain some nontrivial information about the first-order consequences of
RT2kRTk2. Time permitting, we will also discuss the question whether our results have any relevance for the well-known open problem of characterizing the first-order consequences of
RT22RT22 over the traditional base theory
RCA0RCA0.
In the first part of the talk, we concentrated on Ramsey's Theorem for nn-tuples where n≥3n≥3. In this second part, the focus will be on RT22RT22.
The New York City Category Theory Seminar
Date and Time: Wednesday September 30, 2020, 7:00 - 8:30 PM., on Zoom.
Zoom information will be posted on the web page on the day of the talk http://www.sci.brooklyn.cuny.edu/~noson/CTseminar.htmlSpeaker: David Ellerman, University of Ljubljana.
Title: The Logical Theory of Canonical Maps: The Elements & Distinctions Analysis of the Morphisms, Duality, Canonicity, and Universal Constructions in Sets.
Abstract: Category theory gives a mathematical characterization of naturality but not of canonicity. The purpose of this paper is to develop the logical theory of canonical maps based on the broader demonstration that the dual notions of elements & distinctions are the basic analytical concepts needed to unpack and analyze morphisms, duality, canonicity, and universal constructions in Sets, the category of sets and functions. The analysis extends directly to other Sets-based concrete categories (groups, rings, vector spaces, etc.). Elements and distinctions are the building blocks of the two dual logics, the Boolean logic of subsets and the logic of partitions. The partial orders (inclusion and refinement) in the lattices for the dual logics define morphisms. The thesis is that the maps that are canonical in Sets are the ones that are defined (given the data of the situation) by these two logical partial orders and by the compositions of those maps.
Paper: Available here
http://www.sci.brooklyn.cuny.edu/~noson/Ellerman2020.pdf
- - - - Thursday, Oct 1, 2020 - - - -
- - - - Friday, Oct 2, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, Oct 2, 3pm
The seminar will take place virtually at 3pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. David Aspero, University of East Anglia
TBA
- - - - Other Logic News - - - -
- - - - Web Site - - - -
Find us on the web at:
nylogic.github.io(site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to
jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email
jreitz@nylogic.org.
Wednesday seminar
Prague Set Theory Seminar
9/20/2020 10:49:20
Dear all,
Because of the current COVID-19 epidemic related restrictions there will
be no seminar next week, Wednesday September 23 (students are now
officially not allowed to participate seminars).
As for the following weeks, we will see how he situation develops.
Best,
David
Roman Kossak: Truth, Resplendence, and Directed Graphs with Local Finite Height
Boise Logic and Set Theory Seminar
9/17/2020
[Email the organizer scoskey@boisestate.edu for Zoom meeting number]
Speaker: Roman Kossak (CUNY)
Title: Truth, Resplendence, and Directed Graphs with Local Finite Height
Abstract: Under certain assumptions, a nonstandard model of arithmetic admits an assignment of truth values for all of its sentences, standard and nonstandard. This important result in the model theory of arithmetic was proved in 1981 by Kotlarski, Krajewski and Lachlan, with a proof employing a ``rather exotic proof-theoretic technology." In 2009, Enayat and Viser gave a much more accessible model-theoretic proof. In 2018, Schmerl isolated the graph-theoretic component of the Enayat-Visser proof, by showing that certain infinite graphs have kernels, from which the theorem can be obtained as a straightforward corollary. This story is an excellent example of how mathematics gets simplified. I will explain all basic concepts and I will outline the proof of Shmerl's result.
Schmerl's paper is at: arXiv:1807.11832
Tagged: Roman Kossak
Logic Seminar 16 Sept 2020 17:00 hrs at NUS by Ye Jinhe (Notre Dame)
NUS Logic Seminar
9/15/2020 4:23:06
Invitation to the Logic Seminar at the National University of Singapore
Date: Wednesday, 16 September 2020, 17:00 hrs
Talk via Zoom: https://nus-sg.zoom.us/j/96860201432?pwd=cVdwZmd2clVFaEhaTmJjaGdXMFdmdz09
Meeting ID: 968 6020 1432
Password: Is P=NP?
Speaker: Ye Jinhe
Title: The etale open topology
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Abstract: For any field K, we introduce natural topologies on K-points of
varieties over K, which is defined to be the weakest topology such that etale
morphisms are open. This topology turns out to be natural in a lot of settings.
For example, when K is algebraically closed, it is easy to see that we have
the Zariski topology and it picks up the valuation topology in many Henselian
valued fields. Moreover, many topological properties correspond to the algebraic
properties of the field. As an application, we will show large stable fields
are separably closed, a special case of the stable fields conjecture.
This is joint work with Will Johnson, Chieu-Minh Tran and Erik Walsberg.
This Week in Logic at CUNY
This Week in Logic at CUNY
9/13/2020 22:31:31
This Week in Logic at CUNY:
- - - - Monday, Sep 14, 2020 - - - -
Logic and Metaphysics Workshop
Date: Monday, September 14th, 4.15-6.15
For zoom information, email Yale Weiss at: yweiss@gradcenter.cuny.edu.
Speaker: Chris Scambler (NYU)
Title: Cantor’s Theorem, Modalized
Abstract: I will present a modal axiom system for set theory that (I claim) reconciles mathematics after Cantor with the idea there is only one size of infinity. I’ll begin with some philosophical background on Cantor’s proof and its relation to Russell’s paradox. I’ll then show how techniques developed to treat Russell’s paradox in modal set theory can be generalized to produce set theories consistent with the idea that there’s only one size of infinity.
- - - - Tuesday, Sep 15, 2020 - - - -
Computational Logic Seminar
Fall 2020, on-line meetings
Please send me a request for a link to this talk - Sergei Artemov (sartemov@gc.cuny.edu)Time 2:00 - 4:00 PM Tuesday
September 15, 2020
Speaker: Sergei Artemov, Graduate Center, City University of New York
Title: On Constructive Epistemic Logic
Abstract: A joint paper: S.Artemov and T.Protopopescu, Intuitionistic Epistemic Logic, The Review of Symbolic Logic 9(2):266-298, 2016,
opened the door to a new avenue of active research in constructive epistemic logic. We will present the basics and comment on the current state of these studies.
- - - - Wednesday, Sep 16, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, Sep 16, 5:00pm
The seminar will take place virtually at 5pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Sam Coskey, Boise State University
Classification of countable models of ZFC
In 2009 Roman Kossak and I showed that the classification of countable models of PA is Borel complete, which means it is as complex as possible. The proof is a straightforward application of Gaifman’s canonical I-models. In 2017 Sam Dworetzky, John Clemens, and I showed that the argument may also be used to show the classification of countable models of ZFC is Borel complete too. In this talk I'll outline the original argument for models of PA, the adaptation for models of ZFC, and briefly consider several subclasses of countable models of ZFC.
Speaker: Rick Jardine, University of Western Ontario.
Title: Posets, metric spaces, and topological data analysis.
Abstract: Traditional TDA is the analysis of homotopy invariants of systems of spaces V(X) that arise from finite metric spaces X, via distance measures. These spaces can be expressed in terms of posets, which are barycentric subdivisions of the usual Vietoris-Rips complexes V(X). The proofs of stability theorems in TDA are sharpened considerably by direct use of poset techniques.
Expanding the domain of definition to extended pseudo metric spaces enables the construction of a realization functor on diagrams of spaces, which has a right adjoint Y |--> S(Y), called the singular functor. The realization of the Vietoris-Rips system V(X) for an ep-metric space X is the space itself. The counit of the adjunction defines a map \eta: V(X) --> S(X), which is a sectionwise weak equivalence - the proof uses simplicial approximation techniques.
This is the context for the Healy-McInnes UMAP construction, which will be discussed if time permits. UMAP is non-traditional: clusters for UMAP are defined by paths through sequences of neighbour pairs, which can be a highly efficient process in practice.
- - - - Thursday, Sep 17, 2020 - - - -
Zoom seminar in Philosophical Logic
Contact Rohit Parikh (rparikh@gc.cuny.edu) for zoom link.Thursday September 17 at 6:30 PM
Larry Moss of Indiana University will speak about Judgment from
the recent book by Diaconis and Skyrms
- - - - Friday, Sep 18, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, Sep 18, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. Arthur Apter, CUNY
UA and the Number of Normal Measures over ℵω+1ℵω+1
The Ultrapower Axiom UA, introduced by Goldberg and Woodin, is known to have many striking consequences. In particular, Goldberg has shown that assuming UA, the Mitchell ordering of normal measures over a measurable cardinal is linear. I will discuss how this result may be used to construct choiceless models of ZF in which the number of normal measures at successors of singular cardinals can be precisely controlled.
Next Week in Logic at CUNY:
- - - - Monday, Sep 21, 2020 - - - -
- - - - Tuesday, Sep 22, 2020 - - - -
- - - - Wednesday, Sep 23, 2020 - - - -
- - - - Thursday, Sep 24, 2020 - - - -
- - - - Friday, Sep 25, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, Sep 25, 11am
The seminar will take place virtually at 11am US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. Ralf Schindler, University of MünsterMartin's Maximum^++ implies the P_max axiom (*)
Forcing axioms spell out the dictum that if a statement can be forced, then it is already true. The P_max axiom (*) goes beyond that by claiming that if a statement is consistent, then it is already true. Here, the statement in question needs to come from a resticted class of statements, and 'consistent' needs to mean 'consistent in a strong sense.' It turns out that (*) is actually equivalent to a forcing axiom, and the proof is by showing that the (strong) consistency of certain theories gives rise to a corresponding notion of forcing producing a model of that theory. This is joint work with D. Asperó building upon earlier work of R. Jensen and (ultimately) Keisler's 'consistency properties'.
- - - - Other Logic News - - - -
- - - - Web Site - - - -
Find us on the web at:
nylogic.github.io(site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
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jreitz@nylogic.org.
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jreitz@nylogic.org.
Wednesday seminar
Prague Set Theory Seminar
9/13/2020 8:47:47
Dear all,
Mirna Džamonja (IHPST CNRS-Université Panthéon-Sorbonne, Paris) will be
visiting the Institute of Mathematics CAS during the upcoming week. She
will give talks both at the Set Theory and Analysis seminar on Tuesday
September 15th at 10 AM and the at the Wednesday seminar. The
announcement for the Tuesday seminar is here:
https://calendar.math.cas.cz/set-theory-and-analysis-actual
The Seminar on Reckoning meets on Wednesday September 16th at 11:00 in
the Institute of Mathematics CAS, Zitna 25.
!!!
In order to be able to comply with the current 2 meters separation rule
the seminar changes location next week. We will meet in the blue lecture
room on the ground floor of the rear building.
!!!
Program: Mirna Džamonja -- On wide Aronszajn trees
Aronszajn trees are a staple of set theory, but there are applications
where the requirement of all levels being countable is of no importance.
This is the case in set-theoretic model theory, where trees of height
and size ω1 but with no uncountable branches play an important role by
being clocks of Ehrenfeucht--Fraïssé games that measure similarity of
model of size ℵ1. We call such trees wide Aronszajn. In this context one
can also compare trees T and T’ by saying that T weakly embeds into T’
if there is a function f that map T into T’ while preserving the strict
order <_T. This order translates into the comparison of winning
strategies for the isomorphism player, where any winning strategy for T’
translates into a winning strategy for T’. Hence it is natural to ask if
there is a largest such tree, or as we would say, a universal tree for
the class of wood Aronszajn trees with weak embeddings. It was known
that there is no such a tree under CH, but in 1994 Mekler and Väänanen
conjectured that there would be under MA(ω1).
In our upcoming JSL paper with Saharon Shelah we prove that this is not
the case: under MA(ω1) there is no universal wide Aronszajn tree.
The talk will discuss that paper. The paper is available on the arxiv
and on line at JSL in the preproof version DOI: 10.1017/jsl.2020.42
Best,
David
Wednesday seminar
Prague Set Theory Seminar
9/13/2020 8:47:47
Dear all,
Mirna Džamonja (IHPST CNRS-Université Panthéon-Sorbonne, Paris) will be
visiting the Institute of Mathematics CAS during the upcoming week. She
will give talks both at the Set Theory and Analysis seminar on Tuesday
September 15th at 10 AM and the at the Wednesday seminar. The
announcement for the Tuesday seminar is here:
https://calendar.math.cas.cz/set-theory-and-analysis-actual
The Seminar on Reckoning meets on Wednesday September 16th at 11:00 in
the Institute of Mathematics CAS, Zitna 25.
!!!
In order to be able to comply with the current 2 meters separation rule
the seminar changes location next week. We will meet in the blue lecture
room on the ground floor of the rear building.
!!!
Program: Mirna Džamonja -- On wide Aronszajn trees
Aronszajn trees are a staple of set theory, but there are applications
where the requirement of all levels being countable is of no importance.
This is the case in set-theoretic model theory, where trees of height
and size ω1 but with no uncountable branches play an important role by
being clocks of Ehrenfeucht--Fraïssé games that measure similarity of
model of size ℵ1. We call such trees wide Aronszajn. In this context one
can also compare trees T and T’ by saying that T weakly embeds into T’
if there is a function f that map T into T’ while preserving the strict
order <_T. This order translates into the comparison of winning
strategies for the isomorphism player, where any winning strategy for T’
translates into a winning strategy for T’. Hence it is natural to ask if
there is a largest such tree, or as we would say, a universal tree for
the class of wood Aronszajn trees with weak embeddings. It was known
that there is no such a tree under CH, but in 1994 Mekler and Väänanen
conjectured that there would be under MA(ω1).
In our upcoming JSL paper with Saharon Shelah we prove that this is not
the case: under MA(ω1) there is no universal wide Aronszajn tree.
The talk will discuss that paper. The paper is available on the arxiv
and on line at JSL in the preproof version DOI: 10.1017/jsl.2020.42
Best,
David
Wednesday seminar
Prague Set Theory Seminar
9/7/2020 4:39:58
Dear all,
The seminar meets on Wednesday September 9th at 11:00 in the Institute
of Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.
The program is not yet determined, walk-in speakers are welcome.
Otherwise we have the usual backup option of me talking about something..
Best,
David
Kyoto University Research Institute for Mathematical Sciences
Set Theory Workshop, November 16-20, 2020
Conference
9/7/2020
Kyoto University Research Institute for Mathematical Sciences
Set Theory Workshop 2020
Set Theory: Reals and Topology
November 16-20, 2020
http://strims2020.sa-suke.com
Call for lectures and participation
Due to the COVID-19 pandemic, the workshop will take place online. This is the first online version of this workshop.
Every year, set theory researchers from Japan and abroad gather at the RIMS (Research Institute for Mathematical Sciences) of Kyoto University and hold an international workshop that brings together both expert and young researchers of set theory. As indicated in the title “Set Theory: Reals and Topology”, the main topic this year is about the developments of set theory and its interaction with combinatorics of the reals and topology.
We encourage both young researchers and experts, from Japan and abroad, to contribute with lectures in any topic of Set Theory (not necessarily in the main topic). We expect participation (even without lecture) of many researchers in the area and graduate students. Registration is required for participation (see details on the webpage).
Registration deadlines:
For contributed lectures: October 1st, 2020.
For participation (without lecture): October 15th, 2020.
Minicourse Speakers
Osvaldo Guzmán (Universidad Nacional Autónoma de México)
Ashutosh Kumar (Indian Institute of Technology Kampur)
Invited Speakers
Martin Goldstern (TU Wien)
Ulises Ariet Ramos-García (Universidad Nacional Autónoma de México)
Organizer:
Diego A. Mejía (Shizuoka University)
Scientific Committee:
Teruyuki Yorioka (Shizuoka University)
Dilip Raghavan (National University of Singapore)
Tagged: Osvaldo Guzmán, Ashutosh Kumar, Martin Goldstern, Ulises Ariet Ramos-García, Diego A. Mejía
This Week in Logic at CUNY
This Week in Logic at CUNY
9/6/2020 20:28:03
This Week in Logic at CUNY:
- - - - Monday, Sep 7, 2020 - - - -
- - - - Tuesday, Sep 8, 2020 - - - -
************************
Computational Logic Seminar
Fall 2020, on-line meetings
Time 2:00 - 4:00 PM Tuesday, September 8, 2020
Please send a request for a link to this talk (unless you are registered of have already sent me a request for the whole semester): sartemov@gc.cuny.eduSpeaker: Melvin Fitting, Graduate Center, City University of New York
Title: About `Binding Modalities'
Abstract:
In classical logic the addition of quantifiers to propositional logic is essentially unique, with some minor variations of course. In modal logic things are not so monolithic. One can quantify over things or over intensions; domains can be the same from possible world to possible world, or shrink, or grow, or follow no pattern, as one moves from a possible world to an accessible one. In 1963 Kripke showed that shrinking or growing domains related to validity of the Barcan and the converse Barcan formulas, but this was a semantic result. Proof theory is trickier. Nested sequents are well behaved, but axiom systems can be unruly. A direct combination of propositional modal axioms and rules with standard quantificational axioms and rules simply proves the converse Barcan formula. It's not easy to get rid of it. Kripke showed how one could do so, but he needed to use a less common axiomatization of the quantifiers. It works, but one has the impression of having a formal proof system with road blocks placed carefully to prevent proofs from veering into the ditch. Some 40 or more years later, justification logic was created by Artemov, and now there are justification systems that correspond to infinitely many different modal logics. The first justification logic was called LP, for logic of proofs. It is related to propositional S4. LP was extended to a quantified version by Artemov and Yavorskaya, with a possible world semantics supplied by Fitting. Subsequently Artemov and Yavorskaya transferred their ideas, concerning what they called binding modalities, back from quantified LP to quantified S4 itself. In the present work we carry their ideas on further to the basic normal modal logic, K, which is not as well-behaved as S4 on these matters. It turns out that this provides a natural intuition for Kripke's non-standard axiomatization from those many years ago. It also relates quite plausibly to the distinction between de re and de dicto. But now the main work is done through a generalization of the modal operator, instead of through a restriction on allowed quantifier axiomatizations.
- - - - Wednesday, Sep 9, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, Sep 9, 3:00pm
The seminar will take place virtually at 3pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Saeideh Bahrami, Institute for Research in Fundamental Sciences, TehranFixed Points of Initial Self-Embeddings of Models of ArithmeticIn 1973, Harvey Friedman proved his striking result on initial self-embeddings of countable nonstandard models of set theory and Peano arithmetic. In this talk, I will discuss my joint work with Ali Enayat focused on the fixed point set of initial self-embeddings of countable nonstandard models of arithmetic. Especially, I will survey the proof of some generalizations of well-known results on the fixed point set of automorphisms of countable recursively saturated models of PAPA, to results about the fixed point set of initial self-embeddings of countable nonstandard models of IΣ1IΣ1.
- - - - Thursday, Sep 10, 2020 - - - -
- - - - Friday, Sep 11, 2020 - - - -
Next Week in Logic at CUNY:
- - - - Monday, Sep 14, 2020 - - - -
Logic and Metaphysics Workshop
Date: Monday, September 14th, 4.15-6.15
For zoom information, email Yale Weiss at: yweiss@gradcenter.cuny.edu.
Speaker: Chris Scambler (NYU)
Title: Cantor’s Theorem, Modalized
Abstract: I will present a modal axiom system for set theory that (I claim) reconciles mathematics after Cantor with the idea there is only one size of infinity. I’ll begin with some philosophical background on Cantor’s proof and its relation to Russell’s paradox. I’ll then show how techniques developed to treat Russell’s paradox in modal set theory can be generalized to produce set theories consistent with the idea that there’s only one size of infinity.
- - - - Tuesday, Sep 15, 2020 - - - -
- - - - Wednesday, Sep 16, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, Sep 16, 5:00pm
The seminar will take place virtually at 5pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Sam Coskey, Boise State University
TBA
- - - - Thursday, Sep 17, 2020 - - - -
- - - - Friday, Sep 18, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, Sep 18, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. Arthur Apter, CUNY
UA and the Number of Normal Measures over ℵω+1ℵω+1
The Ultrapower Axiom UA, introduced by Goldberg and Woodin, is known to have many striking consequences. In particular, Goldberg has shown that assuming UA, the Mitchell ordering of normal measures over a measurable cardinal is linear. I will discuss how this result may be used to construct choiceless models of ZF in which the number of normal measures at successors of singular cardinals can be precisely controlled.
- - - - Other Logic News - - - -
- - - - Web Site - - - -
Find us on the web at:
nylogic.github.io(site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to
jreitz@nylogic.org.
If you have a
logic-related event that you would like included in future mailings, please email
jreitz@nylogic.org.
Logic Seminar 9 Sept 2020 17:00 hrs at NUS by Ming Xiao
NUS Logic Seminar
8/31/2020 21:45:54
Invitation to the Logic Seminar at the National University of Singapore
Date: Wednesday, 9 September 2020, 17:00 hrs
Talk via Zoom: https://nus-sg.zoom.us/j/96860201432?pwd=cVdwZmd2clVFaEhaTmJjaGdXMFdmdz09
Meeting ID: 968 6020 1432
Password: Is P=NP?
Speaker: Ming Xiao
Title: A Borel Chain Condition of T(X)
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Abstract:
In 1948, Horn and Tarski conjectured whether the sigma-finite chain
condition and sigma-bounded chain condition are equivalent. The first
counterexample was given by Thummel in 2012 and then a Borel
counterexample was given by Todorvevic in 2014. Both examples belong to a
class of poset called "Todorvevic ordering" T(X) over topological spaces
X. In this talk, I will illustrate a satisfactory condition for a
topological space X making the corresponding poset T(X) fail to have a
countable Borel partition witnessing the sigma-finite chain condition,
although it may still be witnessed by non-Borel partitions.
The content of this talk is going to be the same as the one I gave in a
seminar at the Chinese Academy of Sciences last year and is also a part of
my Ph.D. dissertation.
This Week in Logic
This Week in Logic at CUNY
8/30/2020 22:30:02
Hi everyone,
Classes started at CUNY last week, and regular mailings of this newsletter will continue through the Fall semester. Please let me know if you have logic-related events at CUNY or elsewhere that you would like to include.
Best regards,
Jonas Reitz
This Week in Logic at CUNY:
- - - - Monday, Aug 31, 2020 - - - -
- - - - Tuesday, Sep 1, 2020 - - - -
- - - - Wednesday, Sep 02, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, Sep 2, 3:00pm
The seminar will take place virtually at 3pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
September 2
Petr Glivický, Universität Salzburg
The ωω-iterated nonstandard extension of NN and Ramsey combinatorics
In the theory of nonstandard methods (traditionally known as nonstandard analysis), each mathematical object (a set) xx has a uniquely determined so called nonstandard extension ∗x∗x. In general, ∗x⊋{∗y;y∈x}∗x⊋{∗y;y∈x} - that is, besides the original 'standard' elements ∗y∗y for y∈xy∈x, the set ∗x∗x contains some new 'nonstandard' elements.
For instance, some of the nonstandard elements of ∗R∗R can be interpreted as infinitesimals (there is ε∈∗Rε∈∗R such that 0<ε<1/n0<ε<1/n for all n∈Nn∈N) allowing for nonstandard analysis to be developed in ∗R∗R, while ∗N∗N turns out to be an (at least ℵ1ℵ1-saturated) nonstandard elementary extension of NN (in the language of arithmetic).
While the whole nonstandard real analysis is most naturally developed in ∗R∗R (with just a few advanced topics where using the second extension ∗∗R∗∗R is convenient, though far from necessary), recent successful applications of nonstandard methods in combinatorics on NN have utilized also higher order extensions (n)∗N=∗∗∗⋯∗N(n)∗N=∗∗∗⋯∗N with the chain ∗∗∗⋯∗∗∗∗⋯∗ of length n>2n>2.
In this talk we are going to study the structure of the ωω-iterated nonstandard extension ⋅N=⋃n∈ω(n)∗N⋅N=⋃n∈ω(n)∗N of NN and show how the obtained results shed new light on the complexities of Ramsey combinatorics on NN and allow us to drastically simplify proofs of many advanced Ramsey type theorems such as Hindmann's or Milliken's and Taylor's.
- - - - Thursday, Sep 03, 2020 - - - -
Seminar in philosophical logic
Thursday, Sep 3, 6:30pm
Rohit Parikh, City University of New York
On September 3 I will give a talk in the Zoom seminar in philosophical logic which takes place on Thursdays at 6:30 PM.
I will speak about the Sorites paradox and vagueness, relying on previous work by Michael Dummett, Kit Fine, Lotfi Zadeh and myself. I hope you will find it enjoyable.
Join Zoom Meeting
Meeting ID: 896 2345 5996
Passcode: 143539
- Rohit Parikh
- - - - Friday, Sep 04, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, Sep 4, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. Mirna Džamonja, IHPST, CNRS-Université Panthéon-Sorbonne Paris, FranceOn logics that make a bridge from the Discrete to the ContinuousWe study logics which model the passage between an infinite sequence of finite models to an uncountable limiting object, such as is the case in the context of graphons. Of particular interest is the connection between the countable and the uncountable object that one obtains as the union versus the combinatorial limit of the same sequence.Next Week in Logic at CUNY:
- - - - Monday, Sep 7, 2020 - - - -
- - - - Tuesday, Sep 8, 2020 - - - -
- - - - Wednesday, Sep 9, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, Sep 9, 3:00pm
The seminar will take place virtually at 3pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Saeideh Bahrami, Institute for Research in Fundamental Sciences, TehranFixed Points of Initial Self-Embeddings of Models of ArithmeticIn 1973, Harvey Friedman proved his striking result on initial self-embeddings of countable nonstandard models of set theory and Peano arithmetic. In this talk, I will discuss my joint work with Ali Enayat focused on the fixed point set of initial self-embeddings of countable nonstandard models of arithmetic. Especially, I will survey the proof of some generalizations of well-known results on the fixed point set of automorphisms of countable recursively saturated models of PAPA, to results about the fixed point set of initial self-embeddings of countable nonstandard models of IΣ1IΣ1.
- - - - Thursday, Sep 10, 2020 - - - -
- - - - Friday, Sep 11, 2020 - - - -
- - - - Other Logic News - - - -
- - - - Web Site - - - -
Find us on the web at:
nylogic.github.io(site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to
jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email
jreitz@nylogic.org.
Wednesday seminar
Prague Set Theory Seminar
8/27/2020 6:04:35
Dear all,
The seminar meets on Wednesday September 2nd at 11:00 in the Institute
of Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.
Program: David Uhrik -- Partition relations on omega_2
I will present Baumgartner's proof (paper attached) of the consistency
of the partition relation omega_2 --> (omega_2, omega : 2)^2 without
using large cardinals and talk about related results.
Best,
David
Logic Seminar 26 Aug 2020 17:00 hrs at NUS
NUS Logic Seminar
8/23/2020 22:32:40
Invitation to the Logic Seminar at the National University of Singapore
Date: Wednesday, 26 August 2020, 17:00 hrs
Talk via Zoom: https://nus-sg.zoom.us/j/96860201432?pwd=cVdwZmd2clVFaEhaTmJjaGdXMFdmdz09
Meeting ID: 968 6020 1432
Password: Is P=NP?
Speaker: Gordon Hoi
Title: A Faster Exact Algorithm to Count X3SAT Solutions
Abstract: The Exact Satisfiability problem, XSAT, is defined as the
problem of finding a satisfying assignment to a formula in CNF such
that there is exactly one literal in each clause assigned to be 1 and
the other literals in the same clause are set to 0. If we restrict
the length of each clause to be at most 3 literals,
then it is known as the X3SAT problem. In this paper, we consider
the problem of counting the number of satisfying assignments to
the X3SAT problem, which is also known as #X3SAT.
The current state of the art exact algorithm to solve #X3SAT
is given by Dahlloef, Jonsson and Beigel and runs in
O(1.1487^n), where n is the number of variables in
the formula. In this paper, we propose an exact algorithm
for the #X3SAT problem that runs in O(1.1120^n) with very few
branching cases to consider, by using a result from Monien
and Preis to give us a bisection width for graphs with at
most degree 3.
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Logic Seminar Login Details
NUS Logic Seminar
8/19/2020 4:50:02
Hello,
Here the details of the logic seminar Zoom logins for this semester
for those who forgot. The seminar starts in 10 minutes. Cristian
Calude will give the talk. It is 17:00 hrs Singapore time.
Best regards, Frank
Join Zoom Meeting
https://nus-sg.zoom.us/j/96860201432?pwd=cVdwZmd2clVFaEhaTmJjaGdXMFdmdz09
Meeting ID: 968 6020 1432
Password: Is P=NP?
Logic Seminar 19 August 2020 17:00 hrs at NUS (Zoom)
NUS Logic Seminar
8/16/2020 23:32:22
Hello, for the logic seminar, there might be some error in the Zoom details.
The correct ones are as follows:
Join Zoom Meeting
https://nus-sg.zoom.us/j/96860201432?pwd=cVdwZmd2clVFaEhaTmJjaGdXMFdmdz09
Meeting ID: 968 6020 1432
Password: Is P=NP?
Wednesday, 17:00 hrs Singapore time (= 21:00 hrs New Zealand time,
18:00 hrs Japan time and 11:00 hrs German time), this week.
Best regards, Frank
Wednesday seminar
Prague Set Theory Seminar
8/14/2020 5:27:34
Dear all,
There is no seminar next week, Wednesday August 19 due to
vacations/holidays.
The seminar the week after that is uncertain (no announcement = no
seminar). The seminar should meet again in September.
Best,
David
Logic Seminar 19 August 2020 17:00 hrs at NUS (Zoom)
NUS Logic Seminar
8/14/2020 3:59:39
Invitation to the Logic Seminar at the National University of Singapore
Date: Wednesday, 19 August 2020, 17:00 hrs
Room: S17#04-06, Department of Mathematics, NUS
Speaker: Cristian Calude
Title: A New Quantum Random Number Generator Certified by Value Indefiniteness
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Abstract:
We present a new ternary QRNG based on measuring located value indefinite
observables with probabilities 1/4,1/2,1/4 and prove that every
sequence generated is maximally unpredictable, 3-bi-immune (a stronger
form of bi-immunity), and its prefixes are Borel normal. The ternary
quantum random digits produced by the QRNG are algorithmically transformed
into quantum random bits using an alphabetic morphism which preserves all
the above properties.
Zoom: 968 6020 1432. Password: "Is P=NP?"
Link: https://nus-sg.zoom.us/j/94862783492?pwd=eUo0aUdialQrZkt1dDlFNnB4QmtDdz09
Logic Seminar Wed 12 August 2020 17:00 hrs at NUS
NUS Logic Seminar
8/10/2020 18:07:22
Invitation to the Logic Seminar at the National University of Singapore
Date: Wednesday, 12 August 2020, 17:00 hrs
Zoom: https://nus-sg.zoom.us/j/94862783492?pwd=eUo0aUdialQrZkt1dDlFNnB4QmtDdz09
Meeting ID: 948 6278 3492
Password: 811969
Speaker: Frank Stephan
Title: Initial Segment Complexity for Measures - Results and Open Problems
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Abstract: The initial segment complexity of a measure mu at n is given by the
sum over all mu(x)*C(x) with x of length n for the plain complexity C and
similarly for the prefix-free Kolmogorov complexity. This talk gives the
basic relations between initial segment complexity and randomness notions
and lists out various open questions which arise from this work. The same
work was presented at the American Institute of Mathematics in this week's
programme on Algorithmic Randomness.
Wednesday seminar
Prague Set Theory Seminar
8/7/2020 11:08:11
Dear all,
The seminar meets on Wednesday August 12th at 11:00 in the Institute of
Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.
Program: David Chodounsky -- Big Ramsey degrees of hypergraphs (continued)
I will continue the talk on big Ramsey degrees of hypergraphs, this time
I plan to give more details of the finiteness proof for the 3-uniform case.
The preprint is now online: https://arxiv.org/abs/2008.00268
Best,
David
Wednesday seminar
Prague Set Theory Seminar
7/31/2020 6:29:06
Dear all,
There is no seminar next week. You might be interested in participating
the Midsummer Combinatorial Workshop instead.
https://kam.mff.cuni.cz/workshops/mcw/
The seminar will meet again on Wednesday August 12th.
Best,
David
This Week in Logic at CUNY
This Week in Logic at CUNY
7/26/2020 22:59:40
This Week in Logic at CUNY:
- - - - Monday, Jul 27, 2020 - - - -
- - - - Tuesday, Jul 28, 2020 - - - -
- - - - Wednesday, Jul 29, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, July 29, 7:00pm
The seminar will take place virtually at 7pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Kameryn Williams, University of Hawai‘i at Mānoa
End-extensions of models of set theory and the Σ1Σ1 universal finite sequence
Recall that if M⊆NM⊆N are models of set theory then NN end-extends MM if NN does not have new elements for sets in MM. In this talk I will discuss a Σ1Σ1-definable finite sequence which is universal for end extensions in the following sense. Consider a computably axiomatizable extension ¯¯¯¯¯¯¯ZFZF¯ of ZFZF. There is a Σ1Σ1-definable finite sequencea0,a1,…,ana0,a1,…,anwith the following properties.
* ZFZF proves that the sequence is finite.
* In any transitive model of ¯¯¯¯¯¯¯ZFZF¯ the sequence is empty.
* If MM is a countable model of ¯¯¯¯¯¯¯ZFZF¯ in which the sequence is ss and t∈Mt∈M is a finite sequence extending ss then there is an end-extension N⊨¯¯¯¯¯¯¯ZFN⊨ZF¯ of MM in which the sequence is exactly tt.
* Indeed, for the previous statements it suffices that M⊨ZFM⊨ZF and end-extends a submodel W⊨¯¯¯¯¯¯¯ZFW⊨ZF¯ of height at least (ωL1)M(ω1L)M.
This universal finite sequence can be used to determine the modal validities of end-extensional set-theoretic potentialism, namely to be exactly the modal theory S4S4. The sequence can also be used to show that every countable model of set theory extends to a model satisfying the end-extensional maximality principle, asserting that any possibly necessary sentence is already true.
This talk is about joint work with Joel David Hamkins. The Σ1Σ1 universal finite sequence is a sister to the Σ2Σ2 universal finite sequence for rank-extensions of Hamkins and Woodin, and both are cousins of Woodin's universal algorithm for arithmetic.
- - - - Thursday, Jul 30, 2020 - - - -
- - - - Friday, Jul 31, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, July 31, 12pm
The seminar will take place virtually at 12pm US Eastern Standard Time. Please email Victoria Gitman for meeting id.
Corey Switzer, CUNYDissertation defense: Alternative Cichoń diagrams and forcing axioms compatible with CHThis dissertation surveys several topics in the general areas of iterated forcing, infinite combinatorics and set theory of the reals. There are two parts. In the first half I consider alternative versions of the Cichoń diagram. First I show that for a wide variety of reduction concepts there is a Cichoń diagram for effective cardinal characteristics relativized to that reduction. As an application I investigate in detail the Cichoń diagram for degrees of constructibility relative to a fixed inner model of ZFC. Then I study generalizations of cardinal characteristics to the space of functions from ωωωω to ωωωω. I prove that these cardinals can be organized into two diagrams analogous to the standard Cichoń diagram show several independence results and investigate their relation to cardinal invariants on omega. In the second half of the thesis I look at forcing axioms compatible with CH. First I consider Jensen's subcomplete and subproper forcing. I generalize these notions to larger classes which are (apparently) much more nicely behaved structurally. I prove iteration and preservation theorems for both classes and use these to produce many new models of the subcomplete forcing axiom. Finally I deal with dee-complete forcing and its associated axiom DCFA. Extending a well-known result of Shelah, I show that if a tree of height ω1ω1 with no branch can be embedded into an ω1ω1 tree, possibly with uncountable branches, then it can be specialized without adding reals. As a consequence I show that DCFA implies there are no Kurepa trees, even if CH fails.
Next Week in Logic at CUNY:
- - - - Monday, Aug 3, 2020 - - - -
- - - - Tuesday, Aug 4, 2020 - - - -
- - - - Wednesday, Aug 5, 2020 - - - -
- - - - Thursday, Aug 6, 2020 - - - -
- - - - Friday, Aug 7, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, Aug 7, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman for meeting id.
Brent Cody, Virginia Commonwealth University
TBA
- - - - Other Logic News - - - -
A number of logic seminars worldwide have moved online, which provides an unprecedented opportunity for wide participation. In addition to this newsletter and our own website,
nylogic.github.io, take a look at the following for more seminar listings:
Online seminars and talks in Logic
A list of existing seminar series with talks available online, and links to recorded talks:
Online Logic Seminar at SIU
Computability Theory and Applications
Oxford Set Theory Seminar
European Set Theory Society
List of upcoming online talks in set theory around the world:
Logic Supergroup (UCONN)
An alliance of logicians in quarantine, comprised of logic groups across the world, hosting virtual talks:
- - - - Web Site - - - -
Find us on the web at:
nylogic.github.io(site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to
jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email
jreitz@nylogic.org.
Wednesday seminar
Prague Set Theory Seminar
7/22/2020 10:21:05
Dear all,
The seminar meets on Wednesday July 29th at 11:00 in the Institute of
Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.
Program: Egbert Thümmel -- There are no tall analytic Ramsey ideals
An ideal I on omega is said to be Ramsey if the partition relation I^+
-> (I^+)_2^2 does hold. Answering a question of Hrušák and Thümmel, we
show that there are no tall analytic Ramsey ideals. We also show that
every analytic ideal is either included in an F_sigma ideal, or it has a
restriction which is Katětov-above the ideal generated by convergent
sequences of rationals.
Best,
David
Logic summer school at Fudan University, August 10-21, 2020
Conference
7/21/2020
We are organising a logic summer school at Fudan University from Aug 10 - Aug 21. It will be delivered via Zoom meeting. In the first week, Prof. Renling Jin will talk about nonstandard analysis (please note that this part will be in Chinese). In the second week, Prof. Ralf Schindler will introduce the proof of Woodin's (∗) axiom from Martin's Maximum++. Participants are encouraged to fill a registration form, and we will send the Zoom meeting ID accordingly.
For more information, we have a webpage for the summer school: http://logic.fudan.edu.cn/event2020/summer.
Tagged: Renling Jin, Ralf Schindler
This Week in Logic at CUNY
This Week in Logic at CUNY
7/19/2020 22:25:59
This Week in Logic at CUNY:
- - - - Monday, Jul 20, 2020 - - - -
- - - - Tuesday, Jul 21, 2020 - - - -
- - - - Wednesday, Jul 22, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, July 22, 8:00pm
The seminar will take place virtually at 8pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Tin Lok Wong, National University of Singapore
Properties preserved in cofinal extensions
Cofinal extensions generally preserve many more properties of a model of arithmetic than their sisters, end extensions. Exactly how much must or can they preserve? The answer is intimately related to how much arithmetic the model can do. I will survey what is known and what is not known about this question, and report on some recent work on this line.
Video
- - - - Thursday, Jul 23, 2020 - - - -
- - - - Friday, Jul 24, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, July 24, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman for meeting id.
Andrew Brooke-Taylor, University of LeedsMeasurable cardinals and limits in the category of setsAn old result of Isbell characterises measurable cardinals in terms of certain canonical limits in the category of sets. After introducing this characterisation, I will talk about recent work with Adamek, Campion, Positselski and Rosicky teasing out the importance of the canonicity for this and related results. The language will be category-theoretic but the proofs will be quite hands-on combinatorial constructions with sets.
Next Week in Logic at CUNY:
- - - - Monday, Jul 27, 2020 - - - -
- - - - Tuesday, Jul 28, 2020 - - - -
- - - - Wednesday, Jul 29, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, July 29, 7:00pm
The seminar will take place virtually at 7pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Kameryn Williams, University of Hawai‘i at Mānoa
End-extensions of models of set theory and the Σ1Σ1 universal finite sequence
Recall that if M⊆NM⊆N are models of set theory then NN end-extends MM if NN does not have new elements for sets in MM. In this talk I will discuss a Σ1Σ1-definable finite sequence which is universal for end extensions in the following sense. Consider a computably axiomatizable extension ¯¯¯¯¯¯¯ZFZF¯ of ZFZF. There is a Σ1Σ1-definable finite sequencea0,a1,…,ana0,a1,…,anwith the following properties.
* ZFZF proves that the sequence is finite.
* In any transitive model of ¯¯¯¯¯¯¯ZFZF¯ the sequence is empty.
* If MM is a countable model of ¯¯¯¯¯¯¯ZFZF¯ in which the sequence is ss and t∈Mt∈M is a finite sequence extending ss then there is an end-extension N⊨¯¯¯¯¯¯¯ZFN⊨ZF¯ of MM in which the sequence is exactly tt.
* Indeed, for the previous statements it suffices that M⊨ZFM⊨ZF and end-extends a submodel W⊨¯¯¯¯¯¯¯ZFW⊨ZF¯ of height at least (ωL1)M(ω1L)M.
This universal finite sequence can be used to determine the modal validities of end-extensional set-theoretic potentialism, namely to be exactly the modal theory S4S4. The sequence can also be used to show that every countable model of set theory extends to a model satisfying the end-extensional maximality principle, asserting that any possibly necessary sentence is already true.
This talk is about joint work with Joel David Hamkins. The Σ1Σ1 universal finite sequence is a sister to the Σ2Σ2 universal finite sequence for rank-extensions of Hamkins and Woodin, and both are cousins of Woodin's universal algorithm for arithmetic.
- - - - Thursday, Jul 30, 2020 - - - -
- - - - Friday, Jul 31, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, July 31, 12pm
The seminar will take place virtually at 12pm US Eastern Standard Time. Please email Victoria Gitman for meeting id.
Corey Switzer, CUNYDissertation defense: Alternative Cichoń diagrams and forcing axioms compatible with CHThis dissertation surveys several topics in the general areas of iterated forcing, infinite combinatorics and set theory of the reals. There are two parts. In the first half I consider alternative versions of the Cichoń diagram. First I show that for a wide variety of reduction concepts there is a Cichoń diagram for effective cardinal characteristics relativized to that reduction. As an application I investigate in detail the Cichoń diagram for degrees of constructibility relative to a fixed inner model of ZFC. Then I study generalizations of cardinal characteristics to the space of functions from ωωωω to ωωωω. I prove that these cardinals can be organized into two diagrams analogous to the standard Cichoń diagram show several independence results and investigate their relation to cardinal invariants on omega. In the second half of the thesis I look at forcing axioms compatible with CH. First I consider Jensen's subcomplete and subproper forcing. I generalize these notions to larger classes which are (apparently) much more nicely behaved structurally. I prove iteration and preservation theorems for both classes and use these to produce many new models of the subcomplete forcing axiom. Finally I deal with dee-complete forcing and its associated axiom DCFA. Extending a well-known result of Shelah, I show that if a tree of height ω1ω1 with no branch can be embedded into an ω1ω1 tree, possibly with uncountable branches, then it can be specialized without adding reals. As a consequence I show that DCFA implies there are no Kurepa trees, even if CH fails.
- - - - Other Logic News - - - -
A number of logic seminars worldwide have moved online, which provides an unprecedented opportunity for wide participation. In addition to this newsletter and our own website,
nylogic.github.io, take a look at the following for more seminar listings:
Online seminars and talks in Logic
A list of existing seminar series with talks available online, and links to recorded talks:
Online Logic Seminar at SIU
Computability Theory and Applications
Oxford Set Theory Seminar
European Set Theory Society
List of upcoming online talks in set theory around the world:
Logic Supergroup (UCONN)
An alliance of logicians in quarantine, comprised of logic groups across the world, hosting virtual talks:
- - - - Web Site - - - -
Find us on the web at:
nylogic.github.io(site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to
jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email
jreitz@nylogic.org.
Wednesday seminar
Prague Set Theory Seminar
7/17/2020 5:41:13
Dear all,
The seminar meets on Wednesday July 22nd at 11:00 in the Institute of
Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.
Program: David Chodounsky -- Big Ramsey degrees of hypergraphs
I will talk about recent developments concerning Big Ramsey degrees of
universal homogeneous hypergraphs. In particular, we may go through a
proof that these are finite in the 3-uniform case.
Best,
David
Wednesday seminar
Prague Set Theory Seminar
7/10/2020 10:08:15
Dear all,
The seminar meets on Wednesday July 15th at 11:00 in the Institute of
Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.
Program: David Uhrik will talk about the paper of Stevo Todorcevic:
Erdős–Kakutani phenomena for paths (attached).
Best,
David
This Week in Logic at CUNY
This Week in Logic at CUNY
7/6/2020 11:13:37
This Week in Logic at CUNY:
- - - - Monday, Jul 6, 2020 - - - -
- - - - Tuesday, Jul 7, 2020 - - - -
- - - - Wednesday, Jul 8, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, July 8, 7:00pm
The seminar will take place virtually at 7pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Corey Switzer, CUNY
Axiomatizing Kaufmann models in strong logics
A Kaufmann model is an ω1ω1-like, recursively saturated, rather classless model of PA. Such models were constructed by Kaufmann under the ♢♢ assumption and then shown to exist in ZFC by Shelah using an absoluteness argument involving the logic Lω1,ω(Q)Lω1,ω(Q) where QQ is the quantifier 'there exists uncountably many…'. It remains an intriguing, if vague, open problem whether one can construct a Kaufmann model in ZFC 'by hand' i.e. without appealing to some form of absoluteness or other very non-constructive methods. In this talk I consider the related problem of axiomatizing Kaufmann models in Lω1,ω(Q)Lω1,ω(Q) and show that this is independent of ZFC. Along the way we'll see that it is also independent of ZFC whether there is an ω1ω1-preserving forcing notion adding a truth predicate to a Kaufmann model.
- - - - Thursday, Jul 9, 2020 - - - -
- - - - Friday, Jul 10, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, July 10, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman for meeting id.
Peter Holy, University of Udine
Uniform large cardinal characterizations and ideals up to measurability
Many prominent large cardinal notions up to measurability can be characterized by the existence of certain ultrafilters for small models of set theory. Most prominently, this includes weakly compact, ineffable, Ramsey and completely ineffable cardinals, but there are many more, and our characterization schemes also give rise to many new natural large cardinal concepts. Moreover, these characterizations allow for the uniform definition of ideals associated to these large cardinals, which agree with the ideals from the set-theoretic literature (for example, the weakly compact, the ineffable, the Ramsey or the completely ineffable ideal) whenever such had been previously established. For many large cardinal notions, we can show that their ordering with respect to direct implication, but also with respect to consistency strength corresponds in a very canonical way to certain relations between their corresponding large cardinal ideals. This is all material from a fairly extensive joint paper with Philipp Luecke, and I will try to provide an overview as well as present some particular results from this paper.
Next Week in Logic at CUNY:
- - - - Monday, Jul 13, 2020 - - - -
- - - - Tuesday, Jul 14, 2020 - - - -
- - - - Wednesday, Jul 15, 2020 - - - -
- - - - Thursday, Jul 16, 2020 - - - -
- - - - Friday, Jul 17, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, July 17, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman for meeting id.
TBA
Kaethe Minden Bard College at Simon's Rock
- - - - Other Logic News - - - -
A number of logic seminars worldwide have moved online, which provides an unprecedented opportunity for wide participation. In addition to this newsletter and our own website,
nylogic.github.io, take a look at the following for more seminar listings:
Online seminars and talks in Logic
A list of existing seminar series with talks available online, and links to recorded talks:
Online Logic Seminar at SIU
Computability Theory and Applications
Oxford Set Theory Seminar
European Set Theory Society
List of upcoming online talks in set theory around the world:
Logic Supergroup (UCONN)
An alliance of logicians in quarantine, comprised of logic groups across the world, hosting virtual talks:
- - - - Web Site - - - -
Find us on the web at:
nylogic.github.io(site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to
jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email
jreitz@nylogic.org.
Wednesday seminar
Prague Set Theory Seminar
7/6/2020 4:37:07
Dear all,
The seminar meets on Wednesday July 8th at 11:00 in the Institute of
Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.
Program: Jan Grebik -- Approximate measurable colorings
We prove that there is an approximate version of Konig's line coloring
theorem and show how to use it to deduce the result of Toth
https://arxiv.org/abs/1906.03137 about Schreier decorations.
Best,
David
Tagged: Jan Grebik
No seminar this week
Toronto Set Theory Seminar
7/2/2020 17:22:00
Hi everyone,
There won't be a seminar this week.
The regular seminar has concluded for this year and will pick up again in the fall. However, if someone would like to speak soon, let me know and I would be happy to organize something.
Have a good summer,
Bill
Wednesday seminar
Prague Set Theory Seminar
6/29/2020 4:40:27
Dear all,
There is no seminar this Wednesday due to vacations, next week it is
most likely going to be the same story (unless announced otherwise).
Working mathematicians can instead join e.g. the online seminars in
Jerusalem and Gainesville.
HUJI seminar
Wednesday July 1, 10:00 CEST
In the next few weeks Tzoor Plotinikov will present Neeman construction
of a model in which Aleph_{omega+1} has the tree property.
Zoom link:
https://huji.zoom.us/j/243676331?pwd=dU02bUVaNC9jRCtvc2lKbVJJZ2lFdz09
Meeting ID: 243 676 331
Password: 058372
University of Florida Logic Seminar
Tuesday June 30, 22:05 CEST
Jordi Lopez-Abad: The Banakh-Sack rank of a weakly compact set
abstract attached
Zoom link: https://ufl.zoom.us/s/7401025557
Best,
David
This Week in Logic at CUNY
This Week in Logic at CUNY
6/28/2020 19:36:06
This Week in Logic at CUNY:
- - - - Monday, Jun 29, 2020 - - - -
- - - - Tuesday, Jun 30, 2020 - - - -
- - - - Wednesday, Jul 1, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, July 1, 7:00pm
The seminar will take place virtually at 7pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Zachiri McKenzie,
Initial self-embeddings of models of set theory: Part II
In the 1973 paper 'Countable models of set theory', H. Friedman's investigation of embeddings between countable models of subsystems of ZF yields the following two striking results:
1. Every countable nonstandard model of PA is isomorphic to a proper initial segment of itself.
2. Every countable nonstandard model of a sufficiently strong subsystem of ZF is isomorphic to a proper initial segment that is a union of ranks of the original model.
Note that, in contrast to PA, in the context of set theory there are three alternative notions of 'initial segment': transitive subclass, transitive subclass that is closed under subsets and rank-initial segment. Paul Gorbow, in his Ph.D. thesis, systematically studies versions of H. Friedman's self-embedding that yield isomorphisms between a countable nonstandard model of set theory and a rank-initial segment of itself. In these two talks I will discuss recent joint work with Ali Enayat that investigates models of set theory that are isomorphic to a transitive subclass of itself. We call the maps witnessing these isomorphisms 'initial self-embeddings'. I will outline a proof of a refinement of H. Friedman's Theorem that guarantees the existence of initial self-embeddings for certain subsystems of ZF without the powerset axiom. I will then discuss several examples including a nonstandard model of ZFC minus the powerset axiom that admits no initial self-embedding, and models that separate the three different notions of self-embedding for models of set theory. Finally, I will discuss two interesting applications of our version of H. Freidman's Theorem. The first of these is a refinement of a result due to Quinsey that guarantees the existence of partially elementary proper transitive subclasses of non-standard models of ZF minus the powerset axiom. The second result shows that every countable model of ZF with a nonstandard natural number is isomorphic to a transitive subclass of the hereditarily countable sets of its own constructible universe.
- - - - Thursday, Jul 2, 2020 - - - -
- - - - Friday, Jul 3, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, July 3, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman for meeting id.
Vera Fischer, University of ViennaMore ZFC inequalities between cardinal invariants
We will discuss some recent ZFC results concerning the generalized Baire spaces, and more specifically the generalized bounding number, relatives of the generalized almost disjointness number, as well as generalized reaping and domination.
Next Week in Logic at CUNY:
- - - - Monday, Jul 6, 2020 - - - -
- - - - Tuesday, Jul 7, 2020 - - - -
- - - - Wednesday, Jul 8, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, July 8, 7:00pm
The seminar will take place virtually at 7pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Corey Switzer, CUNY
Axiomatizing Kaufmann models in strong logics
A Kaufmann model is an ω1ω1-like, recursively saturated, rather classless model of PA. Such models were constructed by Kaufmann under the ♢♢ assumption and then shown to exist in ZFC by Shelah using an absoluteness argument involving the logic Lω1,ω(Q)Lω1,ω(Q) where QQ is the quantifier 'there exists uncountably many…'. It remains an intriguing, if vague, open problem whether one can construct a Kaufmann model in ZFC 'by hand' i.e. without appealing to some form of absoluteness or other very non-constructive methods. In this talk I consider the related problem of axiomatizing Kaufmann models in Lω1,ω(Q)Lω1,ω(Q) and show that this is independent of ZFC. Along the way we'll see that it is also independent of ZFC whether there is an ω1ω1-preserving forcing notion adding a truth predicate to a Kaufmann model.
- - - - Thursday, Jul 9, 2020 - - - -
- - - - Friday, Jul 10, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, July 10, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman for meeting id.
Peter Holy, University of Udine
TBA
- - - - Other Logic News - - - -
A number of logic seminars worldwide have moved online, which provides an unprecedented opportunity for wide participation. In addition to this newsletter and our own website,
nylogic.github.io, take a look at the following for more seminar listings:
Online seminars and talks in Logic
A list of existing seminar series with talks available online, and links to recorded talks:
Online Logic Seminar at SIU
Computability Theory and Applications
Oxford Set Theory Seminar
European Set Theory Society
List of upcoming online talks in set theory around the world:
Logic Supergroup (UCONN)
An alliance of logicians in quarantine, comprised of logic groups across the world, hosting virtual talks:
- - - - Web Site - - - -
Find us on the web at:
nylogic.github.io(site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to
jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email
jreitz@nylogic.org.
This Week in Logic at CUNY
This Week in Logic at CUNY
6/21/2020 22:54:01
This Week in Logic at CUNY:
- - - - Monday, Jun 22, 2020 - - - -
- - - - Tuesday, Jun 23, 2020 - - - -
- - - - Wednesday, Jun 24, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, June 24, 2:00pm
NOTE: 2:00pm START TIME
The seminar will take place virtually at 2pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.Bartosz Wcisło, Polish Academy of Sciences
Tarski boundary III
Truth theories investigate the notion of truth using axiomatic methods. To a fixed base theory (typically Peano Arithmetic PAPA) we add a unary predicate T(x)T(x) with the intended interpretation 'xx is a (code of a) true sentence.' Then we analyse how adding various possible sets of axioms for that predicate affects its behaviour.
One of the aspects which we are trying to understand is which truth-theoretic principles make the added truth predicate 'strong' in that the resulting theory is not conservative over the base theory. Ali Enayat proposed to call this demarcating line between conservative and non-conservative truth theories 'the Tarski boundary.'
Research on Tarski boundary revealed that natural truth theoretic principles extending compositional axioms tend to be either conservative over PAPA or exactly equivalent to the principle of global reflection over AA. It says that sentences provable in PAPA are true in the sense of the predicate TT. This in turn is equivalent to Δ0Δ0 induction for the compositional truth predicate which turns out to be a surprisingly robust theory.
The equivalences between nonconservative truth theories are typically proved by relatively direct ad hoc arguments. However, certain patterns seem common to these proofs. The first one is construction of various arithmetical partial truth predicates which provably in a given theory have better properties than the original truth predicate. The second one is deriving induction for these truth predicates from internal induction, a principle which says that for any arithmetical formula, the set of those elements for which that formula is satisfied under the truth predicate satisfies the usual induction axioms.
As an example of this phenomenon, we will present two proofs. First, we will show that global reflection principle is equivalent to local induction. Global reflection expresses that any sentence provable in PAPA is true. Local induction says that any predicate obtained by restricting truth predicate to sentences of a fixed syntactic complexity cc satisfies full induction. This is an observation due to Mateusz Łełyk and the author of this presentation.
The second example is a result by Ali Enayat who showed that CT0CT0, a theory compositional truth with Δ0Δ0 induction, is arithmetically equivalent to the theory of compositional truth together with internal induction and disjunctive correctness.
This talk is intended as a continuation of 'Tarski boundary II' presentation at the same seminar. However, we will try to avoid excessive assumptions on familiarity with the previous part.
- - - - Thursday, Jun 25, 2020 - - - -
- - - - Friday, Jun 26, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, June 26, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman for meeting id.Joel David Hamkins, Oxford UniversityCategorical cardinalsZermelo famously characterized the models of second-order Zermelo-Fraenkel set theory ZFC2ZFC2 in his 1930 quasi-categoricity result asserting that the models of ZFC2ZFC2 are precisely those isomorphic to a rank-initial segment VκVκ of the cumulative set-theoretic universe VV cut off at an inaccessible cardinal κ.κ. I shall discuss the extent to which Zermelo's quasi-categoricity analysis can rise fully to the level of categoricity, in light of the observation that many of the VκVκ universes are categorically characterized by their sentences or theories. For example, if κκ is the smallest inaccessible cardinal, then up to isomorphism VκVκ is the unique model of ZFC2ZFC2 plus the sentence 'there are no inaccessible cardinals.' This cardinal κκ is therefore an instance of what we call a first-order sententially categorical cardinal. Similarly, many of the other inaccessible universes satisfy categorical extensions of ZFC2ZFC2 by a sentence or theory, either in first or second order. I shall thus introduce and investigate the categorical cardinals, a new kind of large cardinal. This is joint work with Robin Solberg (Oxford).
Next Week in Logic at CUNY:
- - - - Monday, Jun 29, 2020 - - - -
- - - - Tuesday, Jun 30, 2020 - - - -
- - - - Wednesday, Jul 1, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, July 1, 7:00pm
The seminar will take place virtually at 7pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Zachiri McKenzie,
Initial self-embeddings of models of set theory: Part II
In the 1973 paper 'Countable models of set theory', H. Friedman's investigation of embeddings between countable models of subsystems of ZF yields the following two striking results:
1. Every countable nonstandard model of PA is isomorphic to a proper initial segment of itself.
2. Every countable nonstandard model of a sufficiently strong subsystem of ZF is isomorphic to a proper initial segment that is a union of ranks of the original model.
Note that, in contrast to PA, in the context of set theory there are three alternative notions of 'initial segment': transitive subclass, transitive subclass that is closed under subsets and rank-initial segment. Paul Gorbow, in his Ph.D. thesis, systematically studies versions of H. Friedman's self-embedding that yield isomorphisms between a countable nonstandard model of set theory and a rank-initial segment of itself. In these two talks I will discuss recent joint work with Ali Enayat that investigates models of set theory that are isomorphic to a transitive subclass of itself. We call the maps witnessing these isomorphisms 'initial self-embeddings'. I will outline a proof of a refinement of H. Friedman's Theorem that guarantees the existence of initial self-embeddings for certain subsystems of ZF without the powerset axiom. I will then discuss several examples including a nonstandard model of ZFC minus the powerset axiom that admits no initial self-embedding, and models that separate the three different notions of self-embedding for models of set theory. Finally, I will discuss two interesting applications of our version of H. Freidman's Theorem. The first of these is a refinement of a result due to Quinsey that guarantees the existence of partially elementary proper transitive subclasses of non-standard models of ZF minus the powerset axiom. The second result shows that every countable model of ZF with a nonstandard natural number is isomorphic to a transitive subclass of the hereditarily countable sets of its own constructible universe.
- - - - Thursday, Jul 2, 2020 - - - -
- - - - Friday, Jul 3, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, July 3, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman for meeting id.
- - - - Other Logic News - - - -
A number of logic seminars worldwide have moved online, which provides an unprecedented opportunity for wide participation. In addition to this newsletter and our own website,
nylogic.github.io, take a look at the following for more seminar listings:
Online seminars and talks in Logic
A list of existing seminar series with talks available online, and links to recorded talks:
Online Logic Seminar at SIU
Computability Theory and Applications
Oxford Set Theory Seminar
European Set Theory Society
List of upcoming online talks in set theory around the world:
Logic Supergroup (UCONN)
An alliance of logicians in quarantine, comprised of logic groups across the world, hosting virtual talks:
- - - - Web Site - - - -
Find us on the web at:
nylogic.github.io(site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to
jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email
jreitz@nylogic.org.
Set theory seminar this week: Will Brian
Toronto Set Theory Seminar
6/21/2020 11:28:00
Hi everyone,
This week, Will Brian (UNC Charlotte) will speak in the seminar. His title and abstract can be found below.
Title: Limited-information strategies in Banach-Mazur games.
Abstract: The Banach-Mazur game is an infinite-length game played on a topological space X, in which two players take turns choosing members of an infinite decreasing sequence of open sets, the first player trying to ensure that the intersection of this sequence is empty, and the second that it is not. A
limited-information strategy for one of the players is a game plan that, on any given move, depends on only a small part of the game's history. In this talk we will discuss Telg
ársky's conjecture, which asserts roughly that there must be topological spaces where winning strategies for the Banach-Mazur game cannot be too limited, but must rely on large parts of the game's history in a significant way. Recently, it was shown that this conjecture fails in models of set theory satisfying GCH +

. In such models it is always possible for one player to code all information concerning a game's history into a small piece of it. We will discuss these so-called coding strategies, why assuming GCH +

makes them work so well, and what can go wrong in other models of set theory.
The talk will take place on Friday, June 26 from 1:30-3:00 pm EDT on Zoom, follow the link below:
See you there,
Bill
Wednesday seminar
Prague Set Theory Seminar
6/19/2020 8:37:06
Dear all,
The seminar meets on Wednesday June 24th at 11:00 in the Institute of
Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.
Again, the program is not fixed yet, the backup is either me or Egbert
talking about some set theory. (Last time we were looking at the
triangle free Henson graph and some new proofs of Ramsey-like properties.)
Best,
David
Set theory seminar this week: David Schrittesser
Toronto Set Theory Seminar
6/15/2020 13:45:22
Hi everyone,
This week, David Schrittesser (KGRC, University of Vienna) will speak in the seminar.
Title: Higher degrees of madness
Abstract: The notion of mad family can be generalized by replacing the finite ideal by an iterated Fubini product of the finite ideal. While these ideals are more complicated both combinatorially and in terms of Borel complexity, it turns out that the same assumptions of Ramsey theoretic regularity can rule out their existence. We sketch a proof of this and some related results. This talk is a sequel to my last talk at the Fields Institute Seminar.
The talk will take place on Friday, June 19 from 1:30-3:00 pm EDT on Zoom, follow the link below:
See you there,
Bill
This Week in Logic at CUNY
This Week in Logic at CUNY
6/14/2020 20:10:03
This Week in Logic at CUNY:
- - - - Monday, Jun 15, 2020 - - - -
- - - - Tuesday, Jun 16, 2020 - - - -
- - - - Wednesday, Jun 17, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, June 17, 2:00pm
NOTE: 2:00pm START TIME
The seminar will take place virtually at 2pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.Mateusz Łełyk, University of Warsaw
Partial Reflection over Uniform Disquotational Truth
In the context of arithmetic, a reflection principle for a theory Th is a formal way of expressing that all theorems of Th are true. In the presence of a truth predicate for the language of Th this principle can be expressed as a single sentence (called the Global Reflection principle over Th) but most often is met in the form of a scheme consisting of all sentences of the form
∀x(ProvTh(ϕ(˙x))→ϕ(x)).∀x(ProvTh(ϕ(x˙))→ϕ(x)).Obviously such a scheme is not provable in a consistent theory Th. Nevertheless, such soundness assertions are said to provide a natural and justified way of extending ones initial theory.This perspective is nowadays very fruitfully exploited in the context of formal theories of truth. One of the most basic observations is that strong axioms for the notions of truth follow from formally weak types of axiomatizations modulo reflection principles. In such a way compositional axioms are consequences of the uniform disquotational scheme for for the truth predicate, which is
∀xT(ϕ(˙x))≡ϕ(x).∀xT(ϕ(x˙))≡ϕ(x).The above observation is also used in the recent approach to ordinal analysis of theories of predicative strength by Lev Beklemishev and Fedor Pakhomov. The assignment of ordinal notations to theories proceeds via partial reflection principles (for formulae of a fixed ΣnΣn complexity) over (iterated) disquotational scheme. It becomes important to relate theories of this form to fragments of standard theories of truth, in particular the ones based on induction for restricted classes of formulae such as CT0CT0 (the theory of compositional truth with Δ0Δ0-induction for the extended language. The theory was discussed at length in Bartek Wcisło's talk). Beklemishev and Pakhomov leave the following open question:
Is Σ1Σ1-reflection principle over the uniform disquotational scheme provable in CT0CT0?The main goal of our talk is to present the proof of the affirmative answer to this question. The result significantly improves the known fact on the provability of Global Reflection over PA in CT0CT0. During the talk, we explain the theoretical context described above including the information on how the result fits into Beklemishev-Pakhomov project. In the meantime we give a different proof of their characterisation of Δ0Δ0-reflection over the disquotational scheme.
Despite the proof-theoretical flavour of these results, our proofs rests on essentially model-theoretical techniques. The important ingredient is the Arithmetized Completeness Theorem.
- - - - Thursday, Jun 18, 2020 - - - -
- - - - Friday, Jun 19, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, June 19, 2pm
The seminar will take place virtually at 2pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. Boban Velickovic, University of Paris 7
Strong guessing models
The notion of a guessing model introduced by Viale and Weiss. The principle GM(ω2,ω1)GM(ω2,ω1) asserts that there are stationary many guessing models of size ℵ1ℵ1 in HθHθ, for all large enough regular θθ. It follows from PFAPFA and implies many of its structural consequences, however it does not settle the value of the continuum. In search of higher of forcing axioms it is therefore natural to look for extensions and higher versions of this principle. We formulate and prove the consistency of one such statement that we call SGM+(ω3,ω1)SGM+(ω3,ω1).
It has a number of important structural consequences:
- the tree property at ℵ2ℵ2 and ℵ3ℵ3
- the failure of various weak square principles
- the Singular Cardinal Hypothesis
- Mitchell’s Principle: the approachability ideal agrees with the non stationary ideal on the set of cof(ω1)cof(ω1) ordinals in ω2ω2
- Souslin’s Hypothesis
- The negation of the weak Kurepa Hypothesis
- Abraham’s Principles: every forcing which adds a subset of ω2ω2 either adds a real or collapses some cardinals, etc.
The results are joint with my PhD students Rahman Mohammadpour.
Next Week in Logic at CUNY:
- - - - Monday, Jun 22, 2020 - - - -
- - - - Tuesday, Jun 23, 2020 - - - -
- - - - Wednesday, Jun 24, 2020 - - - -
- - - - Thursday, Jun 25, 2020 - - - -
- - - - Friday, Jun 26, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, June 26, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman for meeting id.
Joel David Hamkins, Oxford University
TBA
- - - - Other Logic News - - - -
A number of logic seminars worldwide have moved online, which provides an unprecedented opportunity for wide participation. In addition to this newsletter and our own website,
nylogic.github.io, take a look at the following for more seminar listings:
Online seminars and talks in Logic
A list of existing seminar series with talks available online, and links to recorded talks:
Online Logic Seminar at SIU
Computability Theory and Applications
Oxford Set Theory Seminar
European Set Theory Society
List of upcoming online talks in set theory around the world:
Logic Supergroup (UCONN)
An alliance of logicians in quarantine, comprised of logic groups across the world, hosting virtual talks:
- - - - Web Site - - - -
Find us on the web at:
nylogic.github.io(site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to
jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email
jreitz@nylogic.org.
Wednesday seminar
Prague Set Theory Seminar
6/12/2020 7:56:09
Dear all,
The seminar will meet again next week, on Wednesday June 17th at 11:00
in the Institute of Mathematics CAS, Zitna 25, seminar room, 3rd floor,
front building.
The program is not yet fixed, the default backup is either me or Egbert
Thuemmel talking about definable ideals on omega.
Best,
David
Set theory seminar this week: Jamal Kawach
Toronto Set Theory Seminar
6/8/2020 12:33:06
Hi everyone,
This week, Jamal Kawach (U of T) will speak in the seminar.
Title: Dual Ramsey theory for countable ordinals
Abstract: Using techniques from the theory of topological Ramsey spaces, we prove a dual Ramsey theorem for countable ordinals. Specifically, for each countable ordinal

we define a topological Ramsey space of equivalence relations on

which code equivalence relations on

, up to a necessary restriction on the set of minimal representatives of the equivalence classes. This extends the classical dual Ramsey theorem of Carlson and Simpson. This is joint work with Stevo Todorcevic.
The talk will take place on June 12 from 1:30-3:00 pm EDT on Zoom, follow the link below:
See you there,
Bill
This Week in Logic at CUNY
This Week in Logic at CUNY
6/7/2020 22:13:02
This Week in Logic at CUNY:
- - - - Monday, Jun 8, 2020 - - - -
- - - - Tuesday, Jun 9, 2020 - - - -
- - - - Wednesday, Jun 10, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, June 10, 7:00pm
The seminar will take place virtually at 7pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.Zachiri McKenzie,
Initial self-embeddings of models of set theory: Part II
In the 1973 paper 'Countable models of set theory', H. Friedman's investigation of embeddings between countable models of subsystems of ZF yields the following two striking results:
1. Every countable nonstandard model of PA is isomorphic to a proper initial segment of itself.
2. Every countable nonstandard model of a sufficiently strong subsystem of ZF is isomorphic to a proper initial segment that is a union of ranks of the original model.
Note that, in contrast to PA, in the context of set theory there are three alternative notions of 'initial segment': transitive subclass, transitive subclass that is closed under subsets and rank-initial segment. Paul Gorbow, in his Ph.D. thesis, systematically studies versions of H. Friedman's self-embedding that yield isomorphisms between a countable nonstandard model of set theory and a rank-initial segment of itself. In these two talks I will discuss recent joint work with Ali Enayat that investigates models of set theory that are isomorphic to a transitive subclass of itself. We call the maps witnessing these isomorphisms 'initial self-embeddings'. I will outline a proof of a refinement of H. Friedman's Theorem that guarantees the existence of initial self-embeddings for certain subsystems of ZF without the powerset axiom. I will then discuss several examples including a nonstandard model of ZFC minus the powerset axiom that admits no initial self-embedding, and models that separate the three different notions of self-embedding for models of set theory. Finally, I will discuss two interesting applications of our version of H. Freidman's Theorem. The first of these is a refinement of a result due to Quinsey that guarantees the existence of partially elementary proper transitive subclasses of non-standard models of ZF minus the powerset axiom. The second result shows that every countable model of ZF with a nonstandard natural number is isomorphic to a transitive subclass of the hereditarily countable sets of its own constructible universe.
- - - - Thursday, Jun 11, 2020 - - - -
- - - - Friday, Jun 12, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, June 12, 2pm
The seminar will take place virtually at 2pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. Michał Godziszewski, Munich Center for Mathematical Philosophy
Michał Godziszewski, Munich Center for Mathematical Philosophy
The Multiverse, Recursive Saturation and Well-Foundedness Mirage: Part II
Recursive saturation, introduced by J. Barwise and J. Schlipf is a robust notion which has proved to be important for the study of nonstandard models (in particular, it is ubiquitous in the model theory of axiomatic theories of truth, e.g. in the topic of satisfaction classes, where one can show that if M⊨ZFCM⊨ZFC is a countable ωω-nonstandard model, then MM admits a satisfaction class iff MM is recursively saturated). V. Gitman and J. Hamkins showed in A Natural Model of the Multiverse Axioms that the collection of countable, recursively saturated models of set theory satisfy the so-called Hamkins's Multiverse Axioms. The property that forces all the models in the Multiverse to be recursively saturated is the so-called Well-Foundedness Mirage axiom which asserts that every universe is ωω-nonstandard from the perspective of some larger universe, or to be more precise, that: if a model MM is in the multiverse then there is a model NN in the multiverse such that MM is a set in NN and N⊨′M is ω−nonstandard.'N⊨′M is ω−nonstandard.'. Inspection of the proof led to a question if the recursive saturation could be avoided in the Multiverse by weakening the Well-Foundedness Mirage axiom. Our main results answer this in the positive. We give two different versions of the Well-Foundedness Mirage axiom - what we call Weak Well-Foundedness Mirage (saying that if MM is a model in the Multiverse then there is a model NN in the Multiverse such that M∈NM∈N and N⊨′M is nonstandard.'N⊨′M is nonstandard.'.) and Covering Well-Foundedness Mirage (saying that if MM is a model in the Multiverse then there is a model NN in the Multiverse with K∈NK∈N such that KK is an end-extension of MM and N⊨′K is ω−nonstandard.'N⊨′K is ω−nonstandard.'). I will present constructions of two different Multiverses satisfying these two weakened axioms. This is joint work with V. Gitman. T. Meadows and K. Williams.
Next Week in Logic at CUNY:
- - - - Monday, Jun 15, 2020 - - - -
- - - - Tuesday, Jun 16, 2020 - - - -
- - - - Wednesday, Jun 17, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, June 17, 2:00pm
NOTE: 2:00pm START TIME
The seminar will take place virtually at 2pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.Mateusz Łełyk, University of Warsaw
Partial Reflection over Uniform Disquotational Truth
In the context of arithmetic, a reflection principle for a theory Th is a formal way of expressing that all theorems of Th are true. In the presence of a truth predicate for the language of Th this principle can be expressed as a single sentence (called the Global Reflection principle over Th) but most often is met in the form of a scheme consisting of all sentences of the form
∀x(ProvTh(ϕ(˙x))→ϕ(x)).∀x(ProvTh(ϕ(x˙))→ϕ(x)).Obviously such a scheme is not provable in a consistent theory Th. Nevertheless, such soundness assertions are said to provide a natural and justified way of extending ones initial theory.This perspective is nowadays very fruitfully exploited in the context of formal theories of truth. One of the most basic observations is that strong axioms for the notions of truth follow from formally weak types of axiomatizations modulo reflection principles. In such a way compositional axioms are consequences of the uniform disquotational scheme for for the truth predicate, which is
∀xT(ϕ(˙x))≡ϕ(x).∀xT(ϕ(x˙))≡ϕ(x).The above observation is also used in the recent approach to ordinal analysis of theories of predicative strength by Lev Beklemishev and Fedor Pakhomov. The assignment of ordinal notations to theories proceeds via partial reflection principles (for formulae of a fixed ΣnΣn complexity) over (iterated) disquotational scheme. It becomes important to relate theories of this form to fragments of standard theories of truth, in particular the ones based on induction for restricted classes of formulae such as CT0CT0 (the theory of compositional truth with Δ0Δ0-induction for the extended language. The theory was discussed at length in Bartek Wcisło's talk). Beklemishev and Pakhomov leave the following open question:
Is Σ1Σ1-reflection principle over the uniform disquotational scheme provable in CT0CT0?The main goal of our talk is to present the proof of the affirmative answer to this question. The result significantly improves the known fact on the provability of Global Reflection over PA in CT0CT0. During the talk, we explain the theoretical context described above including the information on how the result fits into Beklemishev-Pakhomov project. In the meantime we give a different proof of their characterisation of Δ0Δ0-reflection over the disquotational scheme.
Despite the proof-theoretical flavour of these results, our proofs rests on essentially model-theoretical techniques. The important ingredient is the Arithmetized Completeness Theorem.
- - - - Thursday, Jun 18, 2020 - - - -
- - - - Friday, Jun 19, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, June 19, 2pm
The seminar will take place virtually at 2pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. Boban Velickovic University of Paris 7
TBA
- - - - Other Logic News - - - -
A number of logic seminars worldwide have moved online, which provides an unprecedented opportunity for wide participation. In addition to this newsletter and our own website,
nylogic.github.io, take a look at the following for more seminar listings:
Online seminars and talks in Logic
A list of existing seminar series with talks available online, and links to recorded talks:
Online Logic Seminar at SIU
Computability Theory and Applications
Oxford Set Theory Seminar
European Set Theory Society
List of upcoming online talks in set theory around the world:
Logic Supergroup (UCONN)
An alliance of logicians in quarantine, comprised of logic groups across the world, hosting virtual talks:
- - - - Web Site - - - -
Find us on the web at:
nylogic.github.io(site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to
jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email
jreitz@nylogic.org.
This Week in Logic at CUNY
6/1/2020 20:41:19
This Week in Logic at CUNY:
- - - - Monday, Jun 1, 2020 - - - -
- - - - Tuesday, Jun 2, 2020 - - - -
- - - - Wednesday, Jun 3, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, June 3, 7:00pm
The seminar will take place virtually at 7pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.Zachiri McKenzie,
Initial self-embeddings of models of set theory: Part I
In the 1973 paper 'Countable models of set theory', H. Friedman's investigation of embeddings between countable models of subsystems of ZF yields the following two striking results:
1. Every countable nonstandard model of PA is isomorphic to a proper initial segment of itself.
2. Every countable nonstandard model of a sufficiently strong subsystem of ZF is isomorphic to a proper initial segment that is a union of ranks of the original model.
Note that, in contrast to PA, in the context of set theory there are three alternative notions of 'initial segment': transitive subclass, transitive subclass that is closed under subsets and rank-initial segment. Paul Gorbow, in his Ph.D. thesis, systematically studies versions of H. Friedman's self-embedding that yield isomorphisms between a countable nonstandard model of set theory and a rank-initial segment of itself. In these two talks I will discuss recent joint work with Ali Enayat that investigates models of set theory that are isomorphic to a transitive subclass of itself. We call the maps witnessing these isomorphisms 'initial self-embeddings'. I will outline a proof of a refinement of H. Friedman's Theorem that guarantees the existence of initial self-embeddings for certain subsystems of ZF without the powerset axiom. I will then discuss several examples including a nonstandard model of ZFC minus the powerset axiom that admits no initial self-embedding, and models that separate the three different notions of self-embedding for models of set theory. Finally, I will discuss two interesting applications of our version of H. Freidman's Theorem. The first of these is a refinement of a result due to Quinsey that guarantees the existence of partially elementary proper transitive subclasses of non-standard models of ZF minus the powerset axiom. The second result shows that every countable model of ZF with a nonstandard natural number is isomorphic to a transitive subclass of the hereditarily countable sets of its own constructible universe.
- - - - Thursday, Jun 4, 2020 - - - -
- - - - Friday, Jun 5, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, June 5, 2pm
The seminar will take place virtually at 2pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. Michał Godziszewski, Munich Center for Mathematical Philosophy
TBA
Next Week in Logic at CUNY:
- - - - Monday, Jun 8, 2020 - - - -
- - - - Tuesday, Jun 9, 2020 - - - -
- - - - Wednesday, Jun 10, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, June 10, 7:00pm
The seminar will take place virtually at 7pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.Zachiri McKenzie,
Initial self-embeddings of models of set theory: Part II
In the 1973 paper 'Countable models of set theory', H. Friedman's investigation of embeddings between countable models of subsystems of ZF yields the following two striking results:
1. Every countable nonstandard model of PA is isomorphic to a proper initial segment of itself.
2. Every countable nonstandard model of a sufficiently strong subsystem of ZF is isomorphic to a proper initial segment that is a union of ranks of the original model.
Note that, in contrast to PA, in the context of set theory there are three alternative notions of 'initial segment': transitive subclass, transitive subclass that is closed under subsets and rank-initial segment. Paul Gorbow, in his Ph.D. thesis, systematically studies versions of H. Friedman's self-embedding that yield isomorphisms between a countable nonstandard model of set theory and a rank-initial segment of itself. In these two talks I will discuss recent joint work with Ali Enayat that investigates models of set theory that are isomorphic to a transitive subclass of itself. We call the maps witnessing these isomorphisms 'initial self-embeddings'. I will outline a proof of a refinement of H. Friedman's Theorem that guarantees the existence of initial self-embeddings for certain subsystems of ZF without the powerset axiom. I will then discuss several examples including a nonstandard model of ZFC minus the powerset axiom that admits no initial self-embedding, and models that separate the three different notions of self-embedding for models of set theory. Finally, I will discuss two interesting applications of our version of H. Freidman's Theorem. The first of these is a refinement of a result due to Quinsey that guarantees the existence of partially elementary proper transitive subclasses of non-standard models of ZF minus the powerset axiom. The second result shows that every countable model of ZF with a nonstandard natural number is isomorphic to a transitive subclass of the hereditarily countable sets of its own constructible universe.
- - - - Thursday, Jun 11, 2020 - - - -
- - - - Friday, Jun 12, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, June 12, 2pm
The seminar will take place virtually at 2pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. Michał Godziszewski, Munich Center for Mathematical Philosophy
TBA
- - - - Other Logic News - - - -
A number of logic seminars worldwide have moved online, which provides an unprecedented opportunity for wide participation. In addition to this newsletter and our own website,
nylogic.github.io, take a look at the following for more seminar listings:
Online seminars and talks in Logic
A list of existing seminar series with talks available online, and links to recorded talks:
Online Logic Seminar at SIU
Computability Theory and Applications
Oxford Set Theory Seminar
European Set Theory Society
List of upcoming online talks in set theory around the world:
Logic Supergroup (UCONN)
An alliance of logicians in quarantine, comprised of logic groups across the world, hosting virtual talks:
- - - - Web Site - - - -
Find us on the web at:
nylogic.github.io(site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to
jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email
jreitz@nylogic.org.
UPDATE - This Week in Logic at CUNY
This Week in Logic at CUNY
5/25/2020 23:23:22
A correction - this Wednesday's talk in the MOPA seminar will take place at 2pm, rather than the usual 7pm.
Best,
Jonas
This Week in Logic at CUNY:
- - - - Monday, May 25, 2020 - - - -
- - - - Tuesday, May 26, 2020 - - - -
- - - - Wednesday, May 27, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, May 27, 2:00pm
NOTE: New time this week only
The seminar will take place virtually at 2pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.Bartosz Wcisło, University of Warsaw
Tarski boundary II
Truth theories investigate the notion of truth with axiomatic methods. To a fixed base theory (typically Peano Arithmetic PAPA) we add a unary predicate T(x)T(x) with the intended interpretation 'xx is a (code of a) true sentence.' Then we analyse how adding various possible sets of axioms for that predicate affects its behaviour.
One of the aspects we are trying to understand is which truth-theoretic principles make the added truth predicate 'strong' in that the resulting theory is not conservative over the base theory. Ali Enayat proposed to call this 'demarcating line' between conservative and non-conservative truth theories 'the Tarski boundary.'
Research on Tarski boundary revealed that natural truth theoretic principles extending compositional axioms tend to be either conservative over PAPA or exactly equivalent to the principle of global reflection over PAPA. It says that sentences provable in PAPA are true in the sense of the predicate TT. This in turn is equivalent to Δ0Δ0 induction for the compositional truth predicate which turns out to be a surprisingly robust theory.
In our talk, we will try to sketch proofs representative of research on Tarski boundary. We will present the proof by Enayat and Visser showing that the compositional truth predicate is conservative over PAPA. We will also try to discuss how this proof forms a robust basis for further conservativeness results.
On the non-conservative side of Tarski boundary, the picture seems less organised, since more arguments are based on ad hoc constructions. However, we will try to show some themes which occur rather repeatedly in these proofs: iterated truth predicates and the interplay between properties of good truth-theoretic behaviour and induction. To this end, we will present the argument that disjunctive correctness together with the internal induction principle for a compositional truth predicate yields the same consequences as Δ0Δ0-induction for the compositional truth predicate (as proved by Ali Enayat) and that it shares arithmetical consequences with global reflection. The presented results are currently known to be suboptimal.
This talk is intended as a continuation of 'Tarski boundary' presentation. However, we will try to avoid excessive assumptions on familiarity with the previous part.
- - - - Thursday, May 28, 2020 - - - -
- - - - Friday, May 29, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, May 29, 2pm
The seminar will take place virtually at 2pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. Kameryn Williams, University of Hawai‘i at Mānoa
The geology of inner mantles
An inner model is a ground if V is a set forcing extension of it. The intersection of the grounds is the mantle, an inner model of ZFC which enjoys many nice properties. Fuchs, Hamkins, and Reitz showed that the mantle is highly malleable. Namely, they showed that every model of set theory is the mantle of a bigger, better universe of sets. This then raises the possibility of iterating the definition of the mantle—the mantle, the mantle of the mantle, and so on, taking intersections at limit stages—to obtain even deeper inner models. Let's call the inner models in this sequence the inner mantles.
In this talk I will present some results about the sequence of inner mantles, answering some questions of Fuchs, Hamkins, and Reitz. Specifically, I will present the following results, analogues of classic results about the sequence of iterated HODs.
1. (Joint with Reitz) Consider a model of set theory and consider an ordinal eta in that model. Then this model has a class forcing extension whose eta-th inner mantle is the model we started out with, where the sequence of inner mantles does not stabilize before eta.
2. It is consistent that the omega-th inner mantle is an inner model of ZF + ¬AC.
3. It is consistent that the omega-th inner mantle is not a definable class, and indeed fails to satisfy Collection.
Next Week in Logic at CUNY:
- - - - Monday, Jun 1, 2020 - - - -
- - - - Tuesday, Jun 2, 2020 - - - -
- - - - Wednesday, Jun 3, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, June 3, 7:00pm
The seminar will take place virtually at 7pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.Zachiri McKenzie,
Initial self-embeddings of models of set theory: Part I
In the 1973 paper 'Countable models of set theory', H. Friedman's investigation of embeddings between countable models of subsystems of ZF yields the following two striking results:
1. Every countable nonstandard model of PA is isomorphic to a proper initial segment of itself.
2. Every countable nonstandard model of a sufficiently strong subsystem of ZF is isomorphic to a proper initial segment that is a union of ranks of the original model.
Note that, in contrast to PA, in the context of set theory there are three alternative notions of 'initial segment': transitive subclass, transitive subclass that is closed under subsets and rank-initial segment. Paul Gorbow, in his Ph.D. thesis, systematically studies versions of H. Friedman's self-embedding that yield isomorphisms between a countable nonstandard model of set theory and a rank-initial segment of itself. In these two talks I will discuss recent joint work with Ali Enayat that investigates models of set theory that are isomorphic to a transitive subclass of itself. We call the maps witnessing these isomorphisms 'initial self-embeddings'. I will outline a proof of a refinement of H. Friedman's Theorem that guarantees the existence of initial self-embeddings for certain subsystems of ZF without the powerset axiom. I will then discuss several examples including a nonstandard model of ZFC minus the powerset axiom that admits no initial self-embedding, and models that separate the three different notions of self-embedding for models of set theory. Finally, I will discuss two interesting applications of our version of H. Freidman's Theorem. The first of these is a refinement of a result due to Quinsey that guarantees the existence of partially elementary proper transitive subclasses of non-standard models of ZF minus the powerset axiom. The second result shows that every countable model of ZF with a nonstandard natural number is isomorphic to a transitive subclass of the hereditarily countable sets of its own constructible universe.
- - - - Thursday, Jun 4, 2020 - - - -
- - - - Friday, Jun 5, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, June 5, 2pm
The seminar will take place virtually at 2pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. Michał Godziszewski, Munich Center for Mathematical Philosophy
TBA
- - - - Other Logic News - - - -
A number of logic seminars worldwide have moved online, which provides an unprecedented opportunity for wide participation. In addition to this newsletter and our own website,
nylogic.github.io, take a look at the following for more seminar listings:
Online seminars and talks in Logic
A list of existing seminar series with talks available online, and links to recorded talks:
Online Logic Seminar at SIU
Computability Theory and Applications
Oxford Set Theory Seminar
European Set Theory Society
List of upcoming online talks in set theory around the world:
Logic Supergroup (UCONN)
An alliance of logicians in quarantine, comprised of logic groups across the world, hosting virtual talks:
- - - - Web Site - - - -
Find us on the web at:
nylogic.github.io(site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to
jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email
jreitz@nylogic.org.
This Week in Logic at CUNY
This Week in Logic at CUNY
5/25/2020 21:55:51
Hi everyone,
The CUNY semester is coming to an end. However, a number of seminars have plans to continue into the summer months. Regular weekly mailings of "This Week in Logic at CUNY" will continue as long as we have events to report!
Best regards,
Jonas
This Week in Logic at CUNY:
- - - - Monday, May 25, 2020 - - - -
- - - - Tuesday, May 26, 2020 - - - -
- - - - Wednesday, May 27, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, May 27, 7:00pm
The seminar will take place virtually at 7pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.Bartosz Wcisło, University of Warsaw
Tarski boundary II
Truth theories investigate the notion of truth with axiomatic methods. To a fixed base theory (typically Peano Arithmetic PAPA) we add a unary predicate T(x)T(x) with the intended interpretation 'xx is a (code of a) true sentence.' Then we analyse how adding various possible sets of axioms for that predicate affects its behaviour.
One of the aspects we are trying to understand is which truth-theoretic principles make the added truth predicate 'strong' in that the resulting theory is not conservative over the base theory. Ali Enayat proposed to call this 'demarcating line' between conservative and non-conservative truth theories 'the Tarski boundary.'
Research on Tarski boundary revealed that natural truth theoretic principles extending compositional axioms tend to be either conservative over PAPA or exactly equivalent to the principle of global reflection over PAPA. It says that sentences provable in PAPA are true in the sense of the predicate TT. This in turn is equivalent to Δ0Δ0 induction for the compositional truth predicate which turns out to be a surprisingly robust theory.
In our talk, we will try to sketch proofs representative of research on Tarski boundary. We will present the proof by Enayat and Visser showing that the compositional truth predicate is conservative over PAPA. We will also try to discuss how this proof forms a robust basis for further conservativeness results.
On the non-conservative side of Tarski boundary, the picture seems less organised, since more arguments are based on ad hoc constructions. However, we will try to show some themes which occur rather repeatedly in these proofs: iterated truth predicates and the interplay between properties of good truth-theoretic behaviour and induction. To this end, we will present the argument that disjunctive correctness together with the internal induction principle for a compositional truth predicate yields the same consequences as Δ0Δ0-induction for the compositional truth predicate (as proved by Ali Enayat) and that it shares arithmetical consequences with global reflection. The presented results are currently known to be suboptimal.
This talk is intended as a continuation of 'Tarski boundary' presentation. However, we will try to avoid excessive assumptions on familiarity with the previous part.
- - - - Thursday, May 28, 2020 - - - -
- - - - Friday, May 29, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, May 29, 2pm
The seminar will take place virtually at 2pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. Kameryn Williams, University of Hawai‘i at Mānoa
The geology of inner mantles
An inner model is a ground if V is a set forcing extension of it. The intersection of the grounds is the mantle, an inner model of ZFC which enjoys many nice properties. Fuchs, Hamkins, and Reitz showed that the mantle is highly malleable. Namely, they showed that every model of set theory is the mantle of a bigger, better universe of sets. This then raises the possibility of iterating the definition of the mantle—the mantle, the mantle of the mantle, and so on, taking intersections at limit stages—to obtain even deeper inner models. Let's call the inner models in this sequence the inner mantles.
In this talk I will present some results about the sequence of inner mantles, answering some questions of Fuchs, Hamkins, and Reitz. Specifically, I will present the following results, analogues of classic results about the sequence of iterated HODs.
1. (Joint with Reitz) Consider a model of set theory and consider an ordinal eta in that model. Then this model has a class forcing extension whose eta-th inner mantle is the model we started out with, where the sequence of inner mantles does not stabilize before eta.
2. It is consistent that the omega-th inner mantle is an inner model of ZF + ¬AC.
3. It is consistent that the omega-th inner mantle is not a definable class, and indeed fails to satisfy Collection.
Next Week in Logic at CUNY:
- - - - Monday, Jun 1, 2020 - - - -
- - - - Tuesday, Jun 2, 2020 - - - -
- - - - Wednesday, Jun 3, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, June 3, 7:00pm
The seminar will take place virtually at 7pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.Zachiri McKenzie,
Initial self-embeddings of models of set theory: Part I
In the 1973 paper 'Countable models of set theory', H. Friedman's investigation of embeddings between countable models of subsystems of ZF yields the following two striking results:
1. Every countable nonstandard model of PA is isomorphic to a proper initial segment of itself.
2. Every countable nonstandard model of a sufficiently strong subsystem of ZF is isomorphic to a proper initial segment that is a union of ranks of the original model.
Note that, in contrast to PA, in the context of set theory there are three alternative notions of 'initial segment': transitive subclass, transitive subclass that is closed under subsets and rank-initial segment. Paul Gorbow, in his Ph.D. thesis, systematically studies versions of H. Friedman's self-embedding that yield isomorphisms between a countable nonstandard model of set theory and a rank-initial segment of itself. In these two talks I will discuss recent joint work with Ali Enayat that investigates models of set theory that are isomorphic to a transitive subclass of itself. We call the maps witnessing these isomorphisms 'initial self-embeddings'. I will outline a proof of a refinement of H. Friedman's Theorem that guarantees the existence of initial self-embeddings for certain subsystems of ZF without the powerset axiom. I will then discuss several examples including a nonstandard model of ZFC minus the powerset axiom that admits no initial self-embedding, and models that separate the three different notions of self-embedding for models of set theory. Finally, I will discuss two interesting applications of our version of H. Freidman's Theorem. The first of these is a refinement of a result due to Quinsey that guarantees the existence of partially elementary proper transitive subclasses of non-standard models of ZF minus the powerset axiom. The second result shows that every countable model of ZF with a nonstandard natural number is isomorphic to a transitive subclass of the hereditarily countable sets of its own constructible universe.
- - - - Thursday, Jun 4, 2020 - - - -
- - - - Friday, Jun 5, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, June 5, 2pm
The seminar will take place virtually at 2pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. Michał Godziszewski, Munich Center for Mathematical Philosophy
TBA
- - - - Other Logic News - - - -
A number of logic seminars worldwide have moved online, which provides an unprecedented opportunity for wide participation. In addition to this newsletter and our own website,
nylogic.github.io, take a look at the following for more seminar listings:
Online seminars and talks in Logic
A list of existing seminar series with talks available online, and links to recorded talks:
Online Logic Seminar at SIU
Computability Theory and Applications
Oxford Set Theory Seminar
European Set Theory Society
List of upcoming online talks in set theory around the world:
Logic Supergroup (UCONN)
An alliance of logicians in quarantine, comprised of logic groups across the world, hosting virtual talks:
- - - - Web Site - - - -
Find us on the web at:
nylogic.github.io(site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to
jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email
jreitz@nylogic.org.
Set theory seminar this week: Michael Hrusak
Toronto Set Theory Seminar
5/25/2020 10:59:31
Hi everyone,
This Friday, Michael Hrusak (UNAM) will speak in our seminar on the Invariant Ideal Axiom.
Abstract: We introduce the Invariant Ideal Axiom and discuss its impact on the structure of countable topological groups. (joint work with Alexander Shibakov)
The talk will take place on May 29 from 1:30-3:00 pm EDT on Zoom, follow the link below:
Bill Chen
Set theory seminar this week: Vinicius de Oliveira Rodrigues
Toronto Set Theory Seminar
5/18/2020 9:32:37
Hi everyone,
This week, the seminar will host Vinicius de Oliveira Rodrigues (University of São Paulo) who will speak about "Pseudocompact hyperspaces of Isbell-Mrówka spaces." The talk will feature some new results obtained after his talk from November.
Abstract: J. Ginsburg has asked what is the relation between the pseudocompactness of the
-th power of a topological space
and the pseudocompactness of its Vietoris Hyperspace,
. M. Hrusak, I. Martínez-Ruiz and F. Hernandez-Hernandez studied this question restricted to Isbell-Mrówka spaces, that is, spaces of the form
where A is an almost disjoint family. Regarding these spaces, if
is pseudocompact, then
is also pseudocompact, and
is pseudocompact iff
is a MAD family. They showed that if the cardinal characteristic
is
, then for every MAD family
,
is pseudocompact, and if the cardinal characteristic
is less than
, there exists a MAD family
such that
is not pseudocompact. They asked if there exists a MAD family
(in ZFC) such that
is pseudocompact.
In this talk, we present some new results on the (consistent) existence of MAD families whose hyperspaces of their Isbell-Mrówka spaces are (or are not) pseudocompact by constructing new examples. Moreover, we give some combinatorial equivalences for every Isbell-Mrówka space from a MAD family having pseudocompact hyperspace. This is a joint work with, O. Guzman, M. Hrusak, S. Todorcevic and A. Tomita.
The talk will take place this Friday, May 22, from 1:30-3:00 pm EDT on Zoom, follow the link below:
Bill Chen
This Week in Logic at CUNY
This Week in Logic at CUNY
5/17/2020 23:27:42
This Week in Logic at CUNY:
- - - - Monday, May 18, 2020 - - - -
- - - - Tuesday, May 19, 2020 - - - -
- - - - Wednesday, May 20, 2020 - - - -
- - - - Thursday, May 21, 2020 - - - -
- - - - Friday, May 22, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, May 15, 2pm
The seminar will take place virtually at 2pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. Ali Enayat, University of Gothenburg
Recursively saturated models of set theory and their close relatives: Part II
A model MM of set theory is said to be 'condensable' if there is an 'ordinal' αα of MM such that the rank initial segment of MM determined by αα is both isomorphic to MM, and an elementary submodel of MM for infinitary formulae appearing in the well-founded part of MM. Clearly if MM is condensable, then MM is ill-founded. The work of Barwise and Schlipf in the mid 1970s showed that countable recursively saturated models of ZF are condensable.
In this two-part talk, we present a number of new results related to condensable models, including the following two theorems.
Theorem 1. Assuming that there is a well-founded model of ZFC plus 'there is an inaccessible cardinal', there is a condensable model MM of ZFC which has the property that every definable element of MM is in the well-founded part of MM (in particular, MM is ωω-standard, and therefore not recursively saturated).
Theorem 2. The following are equivalent for an ill-founded model MM of ZF of any cardinality:
(a) MM is expandable to Gödel-Bernays class theory plus Δ11Δ11-Comprehension.
(b) There is a cofinal subset of 'ordinals' αα of MM such that the rank initial segment of MM determined by αα is an elementary submodel of MM for infinitary formulae appearing in the well-founded part of M.M.
Moreover, if MM is a countable ill-founded model of ZFC, then conditions (a) and (b) above are equivalent to:
(c) MM is expandable to Gödel-Bernays class theory plus Δ11Δ11-Comprehension + Σ12Σ21-Choice.
Next Week in Logic at CUNY:
- - - - Monday, May 25, 2020 - - - -
- - - - Tuesday, May 26, 2020 - - - -
- - - - Wednesday, May 27, 2020 - - - -
- - - - Thursday, May 28, 2020 - - - -
- - - - Friday, May 29, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, May 22, 2pm
The seminar will take place virtually at 2pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. Kameryn Williams, University of Hawai‘i at Mānoa
TBA
- - - - Other Logic News - - - -
A number of logic seminars worldwide have moved online, which provides an unprecedented opportunity for wide participation. In addition to this newsletter and our own website,
nylogic.github.io, take a look at the following for more seminar listings:
Online seminars and talks in Logic
A list of existing seminar series with talks available online, and links to recorded talks:
Online Logic Seminar at SIU
Computability Theory and Applications
Oxford Set Theory Seminar
European Set Theory Society
List of upcoming online talks in set theory around the world:
Logic Supergroup (UCONN)
An alliance of logicians in quarantine, comprised of logic groups across the world, hosting virtual talks:
- - - - Web Site - - - -
Find us on the web at:
nylogic.github.io(site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to
jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email
jreitz@nylogic.org.
This Week in Logic at CUNY
This Week in Logic at CUNY
5/10/2020 21:15:38
This Week in Logic at CUNY:
- - - - Monday, May 11, 2020 - - - -
- - - - Tuesday, May 12, 2020 - - - -
- - - - Wednesday, May 13, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, May 13
The seminar will take place virtually at 7pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. Bounded finite set theory
There is a well-known close logical connection between PA and finite set theory. Is there a set theory that corresponds in an analogous way to bounded arithmetic IΔ0IΔ0? I propose a candidate for such a theory, called IΔ0SIΔ0S, and consider the questions: what set-theoretic axioms can it prove? And given a model M of IΔ0IΔ0 is there a model of IΔ0SIΔ0S whose ordinals are isomorphic to M? The answer is yes if M is a model of Exp; to obtain the answer we use a new way of coding sets by numbers.
- - - - Thursday, May 14, 2020 - - - -
- - - - Friday, May 15, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, May 15, 2pm
The seminar will take place virtually at 2pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. Ali Enayat, University of Gothenburg
Recursively saturated models of set theory and their close relatives: Part I
A model MM of set theory is said to be 'condensable' if there is an 'ordinal' αα of MM such that the rank initial segment of MM determined by αα is both isomorphic to MM, and an elementary submodel of MM for infinitary formulae appearing in the well-founded part of MM. Clearly if MM is condensable, then MM is ill-founded. The work of Barwise and Schlipf in the mid 1970s showed that countable recursively saturated models of ZF are condensable.
In this two-part talk, we present a number of new results related to condensable models, including the following two theorems.
Theorem 1. Assuming that there is a well-founded model of ZFC plus 'there is an inaccessible cardinal', there is a condensable model MM of ZFC which has the property that every definable element of MM is in the well-founded part of MM (in particular, MM is ωω-standard, and therefore not recursively saturated).
Theorem 2. The following are equivalent for an ill-founded model MM of ZF of any cardinality:
(a) MM is expandable to Gödel-Bernays class theory plus Δ11Δ11-Comprehension.
(b) There is a cofinal subset of 'ordinals' αα of MM such that the rank initial segment of MM determined by αα is an elementary submodel of MM for infinitary formulae appearing in the well-founded part of M.M.
Moreover, if MM is a countable ill-founded model of ZFC, then conditions (a) and (b) above are equivalent to:
(c) MM is expandable to Gödel-Bernays class theory plus Δ11Δ11-Comprehension + Σ12Σ21-Choice.
Next Week in Logic at CUNY:
- - - - Monday, May 18, 2020 - - - -
- - - - Tuesday, May 19, 2020 - - - -
- - - - Wednesday, May 20, 2020 - - - -
- - - - Thursday, May 21, 2020 - - - -
- - - - Friday, May 22, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, May 15, 2pm
The seminar will take place virtually at 2pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. Ali Enayat, University of Gothenburg
Recursively saturated models of set theory and their close relatives: Part II
A model MM of set theory is said to be 'condensable' if there is an 'ordinal' αα of MM such that the rank initial segment of MM determined by αα is both isomorphic to MM, and an elementary submodel of MM for infinitary formulae appearing in the well-founded part of MM. Clearly if MM is condensable, then MM is ill-founded. The work of Barwise and Schlipf in the mid 1970s showed that countable recursively saturated models of ZF are condensable.
In this two-part talk, we present a number of new results related to condensable models, including the following two theorems.
Theorem 1. Assuming that there is a well-founded model of ZFC plus 'there is an inaccessible cardinal', there is a condensable model MM of ZFC which has the property that every definable element of MM is in the well-founded part of MM (in particular, MM is ωω-standard, and therefore not recursively saturated).
Theorem 2. The following are equivalent for an ill-founded model MM of ZF of any cardinality:
(a) MM is expandable to Gödel-Bernays class theory plus Δ11Δ11-Comprehension.
(b) There is a cofinal subset of 'ordinals' αα of MM such that the rank initial segment of MM determined by αα is an elementary submodel of MM for infinitary formulae appearing in the well-founded part of M.M.
Moreover, if MM is a countable ill-founded model of ZFC, then conditions (a) and (b) above are equivalent to:
(c) MM is expandable to Gödel-Bernays class theory plus Δ11Δ11-Comprehension + Σ12Σ21-Choice.
- - - - Other Logic News - - - -
A number of logic seminars worldwide have moved online, which provides an unprecedented opportunity for wide participation. In addition to this newsletter and our own website,
nylogic.github.io, take a look at the following for more seminar listings:
Online seminars and talks in Logic
A list of existing seminar series with talks available online, and links to recorded talks:
Online Logic Seminar at SIU
Computability Theory and Applications
Oxford Set Theory Seminar
European Set Theory Society
List of upcoming online talks in set theory around the world:
Logic Supergroup (UCONN)
An alliance of logicians in quarantine, comprised of logic groups across the world, hosting virtual talks:
- - - - Web Site - - - -
Find us on the web at:
nylogic.github.io(site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to
jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email
jreitz@nylogic.org.
Set theory seminar this Friday: Dima Sinapova
Toronto Set Theory Seminar
5/5/2020 8:00:00
Hi everyone,
This week, we will have Dima Sinapova speaking in the seminar. Her talk is entitled "Iteration, reflection, and Prikry forcing."
Abstract: There is an inherent tension between stationary reflection and the failure of SCH. The former is a compactness type principle that follows from large cardinals. The latter is an instance of incompactness, and usually obtained using Prikry forcing. We describe a Prikry style iteration, and use it to force stationary reflection in the presence of not SCH. Then we discuss the situation at smaller cardinals. This is joint work with Alejandro Poveda and Assaf Rinot.
The talk will take place this Friday, May 8, from 1:30-3:00 pm EDT on Zoom, follow the link below:
IMPORTANT NOTE: Due to an upgrade in Zoom security features, we have a new Zoom link and Meeting ID. Please change your bookmarks accordingly.
See you there,
Bill Chen
This Week in Logic at CUNY
This Week in Logic at CUNY
5/4/2020 0:29:42
Hi everyone,
I'm pleased to pass along the following announcement from Joel David Hamkins:
Oxford Set Theory Seminar
I am starting the Oxford Set Theory Seminar, to be held online via Zoom for the foreseeable future. All set theorists are welcome to participate. You can find a schedule of this term's talks at http://jdh.hamkins.org/oxford-set-theory-seminar/ . -Joel
Best,
Jonas
This Week in Logic at CUNY:
- - - - Monday, May 4, 2020 - - - -
- - - - Tuesday, May 5, 2020 - - - -
- - - - Wednesday, May 6, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, May 6, 7:00pm
The seminar will take place virtually at 7pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.May 6
Ali Enayat, University of Gothenburg
The Barwise-Schlipf characterization of recursive saturation of models of PA: Part II
The subject of this two-part talk is a 1975 Barwise-Schlipf landmark paper, whose main theorem asserts that a nonstandard model M of PA is recursively saturated iff M has an expansion to a model of the subsystem Δ11−CA0Δ11−CA0 of second order arithmetic. The impression one gets from reading the Barwise-Schlipf paper is that the left-to-right direction of the theorem is deep since it relies on sophisticated techniques from admissible set theory, and that the other direction is fairly routine.
As it turns out, the exact opposite is the case: the left-to-right direction of the Barwise-Schlipf theorem lends itself to a proof from first principles (as observed independently by Jonathan Stavi and Sol Feferman not long after the appearance of the Barwise-Schmerl paper); and moreover, as recently shown in my joint work with Jim Schmerl, there is a crucial error in the Barwise-Schlipf proof of the right-to-left direction of the theorem, an error that can be circumvented by a rather nontrivial argument. As I will explain, certain results from the joint work of Matt Kaufmann and Jim Schmerl in the mid-1980s on 'lofty' models of arithmetic come in handy for the analysis of the error, and for circumventing it.
In part I, after going over some history, and preliminaries, I will discuss (1) the gap in the Barwise-Schlipf paper, and (2) the aforementioned Feferman-Stavi proof. In part II, I will focus on how the gap can be circumvented with a proof strategy very different from that Barwise and Schlipf.
- - - - Thursday, May 7, 2020 - - - -
- - - - Friday, May 8, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, May 8, 2pm
The seminar will take place virtually at 2pm New York City Time. Please email Victoria Gitman (
vgitman@nylogic.org) for meeting id.
Sandra Müller, University of Vienna
TBA
Next Week in Logic at CUNY:
- - - - Monday, May 11, 2020 - - - -
- - - - Tuesday, May 12, 2020 - - - -
- - - - Wednesday, May 13, 2020 - - - -
- - - - Thursday, May 14, 2020 - - - -
- - - - Friday, May 15, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, May 15, 2pm
The seminar will take place virtually at 2pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id. Ali Enayat, University of Gothenburg
Recursively saturated models of set theory and their close relatives: Part I
A model MM of set theory is said to be 'condensable' if there is an 'ordinal' αα of MM such that the rank initial segment of MM determined by αα is both isomorphic to MM, and an elementary submodel of MM for infinitary formulae appearing in the well-founded part of MM. Clearly if MM is condensable, then MM is ill-founded. The work of Barwise and Schlipf in the mid 1970s showed that countable recursively saturated models of ZF are condensable.
In this two-part talk, we present a number of new results related to condensable models, including the following two theorems.
Theorem 1. Assuming that there is a well-founded model of ZFC plus 'there is an inaccessible cardinal', there is a condensable model MM of ZFC which has the property that every definable element of MM is in the well-founded part of MM (in particular, MM is ωω-standard, and therefore not recursively saturated).
Theorem 2. The following are equivalent for an ill-founded model MM of ZF of any cardinality:
(a) MM is expandable to Gödel-Bernays class theory plus Δ11Δ11-Comprehension.
(b) There is a cofinal subset of 'ordinals' αα of MM such that the rank initial segment of MM determined by αα is an elementary submodel of MM for infinitary formulae appearing in the well-founded part of M.M.
Moreover, if MM is a countable ill-founded model of ZFC, then conditions (a) and (b) above are equivalent to:
(c) MM is expandable to Gödel-Bernays class theory plus Δ11Δ11-Comprehension + Σ12Σ21-Choice.
- - - - Other Logic News - - - -
A number of logic seminars worldwide have moved online, which provides an unprecedented opportunity for wide participation. In addition to this newsletter and our own website,
nylogic.github.io, take a look at the following for more seminar listings:
Oxford Set Theory Seminar
See schedule at:
European Set Theory Society
List of upcoming online talks in set theory around the world:
Logic Supergroup (UCONN)
An alliance of logicians in quarantine, comprised of logic groups across the world, hosting virtual talks:
- - - - Web Site - - - -
Find us on the web at:
nylogic.github.io(site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to
jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email
jreitz@nylogic.org.
Wednesday seminar
Prague Set Theory Seminar
5/3/2020 14:58:37
Dear all,
There are still no seminar in Prague next week. However, the PhD defence
of Jan Grebik will take place on Tuesday, May 5th at 10:00 via Zoom,
https://cesnet.zoom.us/j/98441831119
The defence is public, guests are welcome and expected. More info here:
https://is.cuni.cz/studium/szz_st/index.php?do=detail_kom&kom=28035&term=587734
Let me also add info on the zoom seminars in Jerusalem and Wroclaw next
week, these may be relevant for our usual audience.
Ziemowit Kostana -- Cohen-like poset for adding Fraisse limits
Tuesday May 5, 17:00 CEST
https://us02web.zoom.us/j/85273088816?pwd=RnRJcXc1YnpWL3R2Y1JRWkVGRUJxUT09
Meeting ID: 852 7308 8816
Password: 978458
There exist a natural forcing notion which turns given countable set
into a Fraisse limit of a given Fraisse class. This long-known
phenomenon provided a rough intuition that Fraisse limits, as "generic
structures", have some connections with forcing. The goal of the talk is
to look at some particular instances and possible applications of this idea.
Tsoor Plotnikov -- Proper forcings and side conditions forcings (continued)
Monday May 4, 10:00am CEST
Meeting ID: 995 0029 0990
Password: 789132
Here are links to the files containing the write up of the two previous
talks:
https://drive.google.com/file/d/1GkkMmUA8usD-vVw0ybX1M5_eTZhgURcu/view?usp=sharing
https://drive.google.com/file/d/1izDqHGMFcGiQw75TvtyD4jzvi7YS-8EW/view?usp=sharing
Alejandro Poveda -- Sigma-Prikry forcings and their iterations
Wednesday May 6, at 10:00 CEST
Meeting ID: 243 676 331 (no password)
In a joint project with A. Rinot and D. Sinapova we introduce a class of
notions of forcing which we call $\Sigma$-Prikry, and show that many of
the known Prikry-type notions of forcing that centers around singular
cardinals of countable cofinality are $\Sigma$-Prikry. Among these
examples one may find Prikry forcing and its supercompact version,
Gitik-Sharon forcing or the Extender Based Prikry forcing due to Gitik
and Magidor.
Our first result shows that there is a functor $\mathbb{A}(\cdot,\cdot)$
which, given a $\Sigma$-Prikry poset $\mathbb P$ and a name for a
non-reflecting stationary set $\dot{T}$, yields a $\Sigma$-Prikry poset
$\mathbb{A}(\mathbb{P},\dot{T})$ that projects onto $\mathbb P$ and
kills the stationarity of $T$. Afterwards, we develop a viable iteration
scheme for $\Sigma$-Prikry posets.
In this talk I pretend to give an overview of this theory and, if time
permits, present the very first application of the method: namely, the
consistency of a failure of the SCH_\kappa with
$Refl(<\omega,\kappa^+)$, where $\kappa$ is a strong limit singular
cardinal of countable cofinality.
Best,
David
Set theory seminar this week: Paul Szeptycki
Toronto Set Theory Seminar
4/29/2020 19:34:05
Hi everyone,
This Friday, Paul Szeptycki will speak in the seminar. His talk is entitled "Strong convergence properties and an example from a

sequence."
Abstract: We present an example of a space constructed from
)
answering some questions of Arhangel'skii. Coauthors Bill Chen and Cesar Corral-Rojas.
The talk will take place this Friday, May 1, from 1:30-3:00 pm EDT on Zoom, follow the link below:
See you there,
Bill Chen
This Week in Logic at CUNY
This Week in Logic at CUNY
4/26/2020 22:44:39
This Week in Logic at CUNY:
- - - - Monday, Apr 27, 2020 - - - -
- - - - Tuesday, Apr 28, 2020 - - - -
- - - - Wednesday, Apr 29, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, April 29, 7:00pm
The seminar will take place virtually at 7pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.April 29
Ali Enayat, University of Gothenburg
The Barwise-Schlipf characterization of recursive saturation of models of PA
The subject of this talk is a 1975 Barwise-Schlipf landmark paper, whose main theorem asserts that a nonstandard model M of PA is recursively saturated iff M has an expansion to a model of the subsystem Δ11−CA0Δ11−CA0 of second order arithmetic. The impression one gets from reading the Barwise-Schlipf paper is that the left-to-right direction of the theorem is deep since it relies on sophisticated techniques from admissible set theory, and that the other direction is fairly routine.
As it turns out, the exact opposite is the case: the left-to-right direction of the Barwise-Schlipf theorem lends itself to a proof from first principles (as observed independently by Jonathan Stavi and Sol Feferman not long after the appearance of the Barwise-Schmerl paper); and moreover, as recently shown in my joint work with Jim Schmerl, there is a crucial error in the Barwise-Schlipf proof of the right-to-left direction of the theorem, an error that can be circumvented by a rather nontrivial argument. As I will explain, certain results from the joint work of Matt Kaufmann and Jim Schmerl in the mid-1980s on 'lofty' models of arithmetic come in handy for the analysis of the error, and for circumventing it.
- - - - Thursday, Apr 30, 2020 - - - -
- - - - Friday, May 1, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, May 1, 2pm
The seminar will take place virtually at 2pm New York City Time. Please email Victoria Gitman (
vgitman@nylogic.org) for meeting id.
Joan Bagaria Universitat de Barcelona
TBA
Next Week in Logic at CUNY:
- - - - Monday, May 4, 2020 - - - -
- - - - Tuesday, May 5, 2020 - - - -
- - - - Wednesday, May 6, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, May 6, 7:00pm
The seminar will take place virtually at 7pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.May 6
Ali Enayat, University of Gothenburg
The Barwise-Schlipf characterization of recursive saturation of models of PA, part 2
The subject of this talk is a 1975 Barwise-Schlipf landmark paper, whose main theorem asserts that a nonstandard model M of PA is recursively saturated iff M has an expansion to a model of the subsystem Δ11−CA0Δ11−CA0 of second order arithmetic. The impression one gets from reading the Barwise-Schlipf paper is that the left-to-right direction of the theorem is deep since it relies on sophisticated techniques from admissible set theory, and that the other direction is fairly routine.
As it turns out, the exact opposite is the case: the left-to-right direction of the Barwise-Schlipf theorem lends itself to a proof from first principles (as observed independently by Jonathan Stavi and Sol Feferman not long after the appearance of the Barwise-Schmerl paper); and moreover, as recently shown in my joint work with Jim Schmerl, there is a crucial error in the Barwise-Schlipf proof of the right-to-left direction of the theorem, an error that can be circumvented by a rather nontrivial argument. As I will explain, certain results from the joint work of Matt Kaufmann and Jim Schmerl in the mid-1980s on 'lofty' models of arithmetic come in handy for the analysis of the error, and for circumventing it.
- - - - Thursday, May 7, 2020 - - - -
- - - - Friday, May 8, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, May 8, 2pm
The seminar will take place virtually at 2pm New York City Time. Please email Victoria Gitman (
vgitman@nylogic.org) for meeting id.
Sandra Müller, University of Vienna
TBA
- - - - Other Logic News - - - -
A number of logic seminars worldwide have moved online, which provides an unprecedented opportunity for wide participation. In addition to this newsletter and our own website,
nylogic.github.io, take a look at the following for more seminar listings:
European Set Theory Society
List of upcoming online talks in set theory around the world:
Logic Supergroup (UCONN)
An alliance of logicians in quarantine, comprised of logic groups across the world, hosting virtual talks:
- - - - Web Site - - - -
Find us on the web at:
nylogic.github.io(site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to
jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email
jreitz@nylogic.org.
Wednesday seminar
Prague Set Theory Seminar
4/26/2020 7:35:09
Dear all,
Still no seminars in Prague next week, I am forwarding info about
relevant online seminars and about the PhD thesis defense of Jan Grebik.
The Jerusalem basic concepts seminar will continue on Monday April 27th
at 11 AM Israel time (= 10 AM CEST).
Tsoor Plotnikov will continue the series of talks on Proper forcings and
side conditions.
The Zoom link for the seminar is
Meeting Link:
https://huji.zoom.us/j/99500290990?pwd=K0RYOTVHdlUzd2JURys0RVI3Znd0UT09
Meeting ID: 995 0029 0990
Password: 789132
On Tuesday April 28th at 17:00 Aleksandra Kwiatkowska will give a talk
on "Simplicity of the automorphism groups of homogeneous structures" at
the Wroclaw seminar. If you are interested, ask Piotr Borodulin-Nadzieja
or me for the Zoom link.
The PhD defense of Jan Grebik will take place next Tuesday, May 5th at
10:00 via Zoom, https://cesnet.zoom.us/j/98441831119
The defense is public, guests are welcome and expected. More info here:
https://is.cuni.cz/studium/szz_st/index.php?do=detail_kom&kom=28035&term=587734
Best,
David
On 16/04/2020 12:40, David Chodounsky wrote:
> Dear all,
>
> Still no seminars seminars in Prague in the foreseeable future.
> However, there are interesting set theory online seminar in Jerusalem
> next week, see the forwarded email (note that the times refers to the
> Israel time zone).
>
> Best,
> David
>
>
>
>
> -------- Forwarded Message --------
> Subject: Set Theory seminars next week
> Date: Wed, 15 Apr 2020 20:38:09 +0000
> From: Menachem Magidor
>
>
> The schedule for the set theory seminars (of course via ZOOM) for next
> week is as follows
>
> 1. *The basic learning seminar
> *The seminar will be held on Monday April 20th at 11 am.
> Tsur Plotnikov will start a series of talk about side conditions
> forcing of two types and PFA.
> As introduction the talks will include some basic facts about
> proper forcings.
>
> The Zoom meeting ID for this seminar will be 995 0029 0990 and the
> password is 789132
>
>
> 2. The regular Wednesday seminar will be held on Wednesday April 22nd
> at 11 am.
> Jing Zhang will speak about
> Title: Transformations of the transfinite plane
> Abstract: We discuss the existence of certain transformation functions
> turning pairs of ordinals into triples (or pairs) of ordinals, that
> allows reductions of complicated Ramsey theoretic problems into simpler
> ones. We will focus on the existence of various kinds of strong
> colorings. The basic technique is Todorcevic's walks on ordinals. Joint
> work with Assaf Rinot.
>
> The Zoom meeting ID is 243-676-331
> and no password.
>
> Best
> Menachem Magidor
Wednesday seminar
Prague Set Theory Seminar
4/26/2020 7:35:09
Dear all,
Still no seminars in Prague next week, I am forwarding info about
relevant online seminars and about the PhD thesis defense of Jan Grebik.
The Jerusalem basic concepts seminar will continue on Monday April 27th
at 11 AM Israel time (= 10 AM CEST).
Tsoor Plotnikov will continue the series of talks on Proper forcings and
side conditions.
The Zoom link for the seminar is
Meeting Link:
https://huji.zoom.us/j/99500290990?pwd=K0RYOTVHdlUzd2JURys0RVI3Znd0UT09
Meeting ID: 995 0029 0990
Password: 789132
On Tuesday April 28th at 17:00 Aleksandra Kwiatkowska will give a talk
on "Simplicity of the automorphism groups of homogeneous structures" at
the Wroclaw seminar. If you are interested, ask Piotr Borodulin-Nadzieja
or me for the Zoom link.
The PhD defense of Jan Grebik will take place next Tuesday, May 5th at
10:00 via Zoom, https://cesnet.zoom.us/j/98441831119
The defense is public, guests are welcome and expected. More info here:
https://is.cuni.cz/studium/szz_st/index.php?do=detail_kom&kom=28035&term=587734
Best,
David
On 16/04/2020 12:40, David Chodounsky wrote:
> Dear all,
>
> Still no seminars seminars in Prague in the foreseeable future.
> However, there are interesting set theory online seminar in Jerusalem
> next week, see the forwarded email (note that the times refers to the
> Israel time zone).
>
> Best,
> David
>
>
>
>
> -------- Forwarded Message --------
> Subject: Set Theory seminars next week
> Date: Wed, 15 Apr 2020 20:38:09 +0000
> From: Menachem Magidor
>
>
> The schedule for the set theory seminars (of course via ZOOM) for next
> week is as follows
>
> 1. *The basic learning seminar
> *The seminar will be held on Monday April 20th at 11 am.
> Tsur Plotnikov will start a series of talk about side conditions
> forcing of two types and PFA.
> As introduction the talks will include some basic facts about
> proper forcings.
>
> The Zoom meeting ID for this seminar will be 995 0029 0990 and the
> password is 789132
>
>
> 2. The regular Wednesday seminar will be held on Wednesday April 22nd
> at 11 am.
> Jing Zhang will speak about
> Title: Transformations of the transfinite plane
> Abstract: We discuss the existence of certain transformation functions
> turning pairs of ordinals into triples (or pairs) of ordinals, that
> allows reductions of complicated Ramsey theoretic problems into simpler
> ones. We will focus on the existence of various kinds of strong
> colorings. The basic technique is Todorcevic's walks on ordinals. Joint
> work with Assaf Rinot.
>
> The Zoom meeting ID is 243-676-331
> and no password.
>
> Best
> Menachem Magidor
Set theory seminar this week: Todd Eisworth
Toronto Set Theory Seminar
4/21/2020 13:36:18
Hi everyone,
This Friday, Todd Eisworth (Ohio University) will speak in the seminar on "Representability and pseudopowers."
Abstract: We will prove some basic facts about Shelah’s pseudopower function, and derive some new (?) ZFC results in cardinal arithmetic using basic topological ideas. This talk is designed to be an introduction to this part of pcf theory.
See you there,
Bill Chen
This Week in Logic at CUNY
This Week in Logic at CUNY
4/19/2020 23:21:46
Hi everyone,
A number of logic seminars worldwide have moved online, which provides an unprecedented opportunity for wide participation. In addition to this newsletter and our own website,
nylogic.github.io, take a look at the following for more seminar listings:
European Set Theory Society
List of upcoming online talks in set theory around the world:
Logic Supergroup (UCONN)
An alliance of logicians in quarantine, comprised of logic groups across the world, hosting virtual talks:
Best regards,
Jonas
This Week in Logic at CUNY:
- - - - Monday, Apr 20, 2020 - - - -
- - - - Tuesday, Apr 21, 2020 - - - -
- - - - Wednesday, Apr 22, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, April 22, 7:00pm
The seminar will take place virtually at 7pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Recall that given a complete theory TT and a type p(x)p(x) the Hanf number for p(x)p(x) is the least cardinal κκ so that any model of TT of size κκ realizes p(x)p(x) (if such a κκ exists and ∞∞ otherwise). The Hanf number for TT, denoted H(T)H(T), is the supremum of the successors of the Hanf numbers for all possible types p(x)p(x) whose Hanf numbers are <∞<∞. We have seen so far in the seminar that for any complete, consistent TT in a countable language H(T)≤ℶω1H(T)≤ℶω1 (a result due to Morley). In this talk I will present the following theorems: (1) The Hanf number for true arithmetic is ℶωℶω (Abrahamson-Harrington-Knight) but (2) the Hanf number for False Arithmetic is ℶω1ℶω1 (Abrahamson-Harrington)
- - - - Thursday, Apr 23, 2020 - - - -
- - - - Friday, Apr 24, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, April 24, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (
vgitman@nylogic.org) for meeting id.
Arthur Apter, CUNY
Indestructibility and the First Two Strongly Compact Cardinals
Starting from a model of ZFC with two supercompact cardinals, I will discuss how to force and construct a model in which the first two strongly compact cardinals κ1κ1 and κ2κ2 are also the first two measurable cardinals. In this model, κ1κ1's strong compactness is indestructible under arbitrary κ1κ1-directed closed forcing, and κ2κ2's strong compactness is indestructible under Add(κ2,λ)Add(κ2,λ) for any ordinal λλ. This answers a generalized version of a question of Sargsyan.
Next Week in Logic at CUNY:
- - - - Monday, Apr 27, 2020 - - - -
- - - - Tuesday, Apr 28, 2020 - - - -
- - - - Wednesday, Apr 29, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, April 29, 7:00pm
The seminar will take place virtually at 7pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.April 29
Ali Enayat, University of Gothenburg
The Barwise-Schlipf characterization of recursive saturation of models of PA
The subject of this talk is a 1975 Barwise-Schlipf landmark paper, whose main theorem asserts that a nonstandard model M of PA is recursively saturated iff M has an expansion to a model of the subsystem Δ11−CA0Δ11−CA0 of second order arithmetic. The impression one gets from reading the Barwise-Schlipf paper is that the left-to-right direction of the theorem is deep since it relies on sophisticated techniques from admissible set theory, and that the other direction is fairly routine.
As it turns out, the exact opposite is the case: the left-to-right direction of the Barwise-Schlipf theorem lends itself to a proof from first principles (as observed independently by Jonathan Stavi and Sol Feferman not long after the appearance of the Barwise-Schmerl paper); and moreover, as recently shown in my joint work with Jim Schmerl, there is a crucial error in the Barwise-Schlipf proof of the right-to-left direction of the theorem, an error that can be circumvented by a rather nontrivial argument. As I will explain, certain results from the joint work of Matt Kaufmann and Jim Schmerl in the mid-1980s on 'lofty' models of arithmetic come in handy for the analysis of the error, and for circumventing it.
- - - - Thursday, Apr 30, 2020 - - - -
- - - - Friday, May 1, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, May 1, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (
vgitman@nylogic.org) for meeting id.
Joan Bagaria Universitat de Barcelona
TBA
- - - - Other Logic News - - - -
- - - - Web Site - - - -
Find us on the web at:
nylogic.github.io(site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to
jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email
jreitz@nylogic.org.
Wednesday seminar
Prague Set Theory Seminar
4/16/2020 6:40:24
Dear all,
Still no seminars seminars in Prague in the foreseeable future.
However, there are interesting set theory online seminar in Jerusalem
next week, see the forwarded email (note that the times refers to the
Israel time zone).
Best,
David
-------- Forwarded Message --------
Subject: Set Theory seminars next week
Date: Wed, 15 Apr 2020 20:38:09 +0000
From: Menachem Magidor
The schedule for the set theory seminars (of course via ZOOM) for next
week is as follows
1. *The basic learning seminar
*The seminar will be held on Monday April 20th at 11 am.
Tsur Plotnikov will start a series of talk about side conditions
forcing of two types and PFA.
As introduction the talks will include some basic facts about
proper forcings.
The Zoom meeting ID for this seminar will be 995 0029 0990 and the
password is 789132
2. The regular Wednesday seminar will be held on Wednesday April 22nd
at 11 am.
Jing Zhang will speak about
Title: Transformations of the transfinite plane
Abstract: We discuss the existence of certain transformation functions
turning pairs of ordinals into triples (or pairs) of ordinals, that
allows reductions of complicated Ramsey theoretic problems into simpler
ones. We will focus on the existence of various kinds of strong
colorings. The basic technique is Todorcevic's walks on ordinals. Joint
work with Assaf Rinot.
The Zoom meeting ID is 243-676-331
and no password.
Best
Menachem Magidor
Wednesday seminar
Prague Set Theory Seminar
4/16/2020 6:40:24
Dear all,
Still no seminars seminars in Prague in the foreseeable future.
However, there are interesting set theory online seminar in Jerusalem
next week, see the forwarded email (note that the times refers to the
Israel time zone).
Best,
David
-------- Forwarded Message --------
Subject: Set Theory seminars next week
Date: Wed, 15 Apr 2020 20:38:09 +0000
From: Menachem Magidor
The schedule for the set theory seminars (of course via ZOOM) for next
week is as follows
1. *The basic learning seminar
*The seminar will be held on Monday April 20th at 11 am.
Tsur Plotnikov will start a series of talk about side conditions
forcing of two types and PFA.
As introduction the talks will include some basic facts about
proper forcings.
The Zoom meeting ID for this seminar will be 995 0029 0990 and the
password is 789132
2. The regular Wednesday seminar will be held on Wednesday April 22nd
at 11 am.
Jing Zhang will speak about
Title: Transformations of the transfinite plane
Abstract: We discuss the existence of certain transformation functions
turning pairs of ordinals into triples (or pairs) of ordinals, that
allows reductions of complicated Ramsey theoretic problems into simpler
ones. We will focus on the existence of various kinds of strong
colorings. The basic technique is Todorcevic's walks on ordinals. Joint
work with Assaf Rinot.
The Zoom meeting ID is 243-676-331
and no password.
Best
Menachem Magidor
Set theory seminar this week: Matteo Viale
Toronto Set Theory Seminar
4/14/2020 8:00:00
Hi everyone,
This Friday, Matteo Viale (University of Torino) will speak in the seminar. His talk is entitled "Tameness for set theory."
Abstract: We show that (assuming large cardinals) set theory is a tractable (and we dare to say tame) first order theory when formalized in a first order signature with natural predicate symbols for the basic definable concepts of second and third order arithmetic, and appealing to the model-theoretic notions of model completeness and model companionship.
Specifically we develop a general framework linking generic absoluteness results to model companionship and show that (with the required care in details) a
-property formalized in an appropriate language for second or third order number theory is forcible from some T extending ZFC + large cardinals if and only if it is consistent with the universal fragment of T if and only if it is realized in the model companion of T.
Part (but not all) of our results are conditional to the proof of Schindler and Asperò that Woodin’s axiom (*) can be forced by a stationary set preserving forcing.
Have a good week,
Bill Chen
This Week in Logic at CUNY
This Week in Logic at CUNY
4/12/2020 21:58:13
Hi everyone,
I'm very pleased to announce that some seminars are continuing virtually during this turbulent time. Regular weekly mailings of "This Week in Logic" will resume until further notice!
Best regards,
Jonas
This Week in Logic at CUNY:
- - - - Monday, Apr 13, 2020 - - - -
- - - - Tuesday, Apr 14, 2020 - - - -
- - - - Wednesday, Apr 15, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, April 15, 7:00pm
The seminar will take place virtually at 7pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.Wei Wang, Institute of Logic and Cognition, Sun Yat-sen University
Non-standard models of arithmetic and their standard systems
PA is the first order fragment of Peano's axiomatization of the natural numbers. The natural numbers, N, is called the standard model of PA. But by compactness theorem in first order logic, there are also models of PA different from N, which are called non-standard models of arithmetic. Like in N, every element of a non-standard model M has a binary expansion, which can be regarded as the characteristic function of a subset of N. The standard system of M is the collection of all such subsets of N. It is known that standard systems of non-standard models are always Scott sets and every Scott set of cardinality less than or equal to the first uncountable cardinal is the standard system of some non-standard model. However, the general Scott set problem, whether every Scott set is the standard system of some non-standard model, remains one of the major open problems in the model theory of arithmetic. This talk will present some history of Scott set problem, as well as two constructions of non-standard models with uncountable standard systems.
- - - - Thursday, Apr 16, 2020 - - - -
- - - - Friday, Apr 17, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, April 17, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Corey Switzer, CUNYSpecializing Wide Trees Without Adding Reals
An important advancement in iterated forcing was Jensen’s proof that CH does not imply ♢♢ by iteratively specializing Aronszajn trees with countable levels without adding reals thus producing a model of CH plus 'all Aronszajn trees are special'. This proof was improved by Shelah who developed a general method around the notion of dee-complete forcing. This class (under certain circumstances) can be iterated with countable support and does not add reals. However, neither Jensen's nor Shelah's posets will specialize trees of uncountable width and it remains unclear when one can iteratively specialize wider trees. Indeed a very intriguing example, due to Todorčević, shows that there is always a wide Aronszajn tree which cannot be specialized without adding reals. By contrast the ccc forcing for specializing Aronszajn trees makes no distinction between trees of different widths (but may add many reals). In this talk we will provide a general criteria a wide trees Aronszajn tree can have that implies the existence of a dee-complete poset specializing it. Time permitting we will discuss applications of this forcing to forcing axioms compatible with CH and some open questions related to set theory of the reals.
Next Week in Logic at CUNY:
- - - - Monday, Apr 20, 2020 - - - -
- - - - Tuesday, Apr 21, 2020 - - - -
- - - - Wednesday, Apr 22, 2020 - - - -
- - - - Thursday, Apr 23, 2020 - - - -
- - - - Friday, Apr 24, 2020 - - - -
- - - - Other Logic News - - - -
- - - - Web Site - - - -
Find us on the web at:
nylogic.github.io(site designed, built & maintained by Victoria Gitman)
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Set theory seminar this week: Keegan Dasilva Barbosa
Toronto Set Theory Seminar
4/7/2020 8:00:00
Hi everyone,
This Friday, Keegan Dasilva Barbosa will speak on A Decomposition Theorem for Aronszajn Lines.
Abstract: We will prove that under the proper forcing axiom, the class of all Aronszajn lines behave like

-scattered orders under the embeddability relation. In particular, we show that the class of better quasi order labeled fragmented Aronszajn lines is itself a better quasi order. Moreover, we show that every better quasi order labeled Aronszajn line can be expressed as a finite sum of labeled types which are algebraically indecomposable. By encoding lines with finite labeled trees, we are also able to deduce a decomposition result, that for every Aronszajn line

, there is an

such that for any finite colouring of

, there is a subset

of

isomorphic to

which uses no more than

colours.
The talk will take place this Friday, April 10, from 1:30-3:00 pm EDT on Zoom, details below:
Topic: Set Theory Seminar
Time: Apr 10, 2020 01:30 PM Eastern Time (US and Canada)
19:30 CEST (Central Europe)
01:30 AM SST (Singapore)
Bill Chen
Logic Seminar Wed 8 April 2020 17:00 hrs at NUS via Zoom
NUS Logic Seminar
4/2/2020 23:49:27
Invitation to the Logic Seminar at the National University of Singapore
Date: Wednesday, 8 April 2020, 17:00 hrs
Zoom: Meeting URL is https://nus-sg.zoom.us/j/786053022 and
Meeting ID is 786 053 022.
Host: Frank Stephan, Department of Mathematics, NUS
Speaker: Wu Guohua.
Title: Members of thin Pi01 classes and their Turing degrees
Abstract: Martin and Pour-El constructed in 1970 a consistent r.e.
theory with few r.e. extensions. Motivated by this work, Cenzer,
Downey, Jockusch and Shore raised the notion of thin Pi01 classes in
their paper in 1993, where a Pi01 class P is thin if every Pi01
subclass of P is the intersection of P and some clopen set. While they
put focus on various Turing degrees of members in these classes, they
also constructed degrees below 0', one r.e., and one minimal,
containing no members of any thin Pi01 classes. In this talk, I will
present basic ideas of the constructions and provide some recent
progress along this topic.
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Set theory seminar this Friday: Iván Ongay Valverde
Toronto Set Theory Seminar
3/31/2020 16:14:47
Hi everyone,
Our seminar returns to break up your social isolation. This week, Iván Ongay Valverde from the University of Wisconsin will speak about Splitting localization and prediction numbers.
Abstract: In 1993, Newelski and Roslanowski studied some cardinal characteristics related to the unsymmetric game (I, as Geschke, called them the localization numbers). While doing this, they found the n-localization property. When a forcing has this property, you can ensure that all new reals are 'tame' somehow (for example, you do not add Cohen or Random reals).
In a different line of study, Andreas Blass worked with some cardinal characteristics related to the idea of guessing correctly a real number given certain amount of information (he called them evasion and prediction numbers). In 2010, it was an open question whether some possible variations of these numbers were known cardinal characteristics or not.
Impressively, these two notions are related.
In this talk, we will show that the k global adaptive prediction numbers are not any other cardinal characteristic. In particular, they are not the localization numbers. To do this, we will use techniques analogue to Newelski and Roslanowski and we will show that the n-localization can be weakened to get their result.
The talk will take place from 1:30-3:00 pm EDT on Zoom, details below.
Zoom Address for the Seminar Talk Next Week Wednesday (Logic Seminar NUS)
NUS Logic Seminar
3/28/2020 2:58:16
Dear participants,
The logic seminar will be held as a Zoom Meeting.
In the case that you want to join, please use the following
link on 1 April 2020 a bit before 17:00 hrs Singapore time:
https://nus-sg.zoom.us/j/138746532
Also note that you might need a meeting ID which I forgot in
the previous email. It is ID 138-746-532.
Best regards, Frank Stephan
> ------------------------------------------------------------------------
> Invitation to the Logic Seminar at the National University of Singapore
>
> Date: Wednesday, 1 April 2020, 17:00 hrs (Singapore Time)
>
> Room: S17#04-06, Department of Mathematics, NUS
>
> Speaker: Frank Stephan
>
> Title: Lower Bounds for the Strong N-Conjecture
>
> Abstract:
> The strong n-conjecture is a generalisation of the abc-conjecture
> concerning the limit superior of qualities of n-tuples of integers which
>
> (1) are pairwise co-prime;
>
> (2) have the sum 0;
>
> (3) do not have nontrivial subsums giving 0.
>
> The quality of a tuple is the logarithm of the largest member (by absolute
> value) divided by the logarithm of the largest square-free divider of the
> product of all members of the tuple. Originally it was conjectured that
> the limit superior of these qualities is 1, see the Wikipedia page at
>
> https://en.wikipedia.org/wiki/N_conjecture
>
> but Konyagin (as reported by Browkin 2000) found already an example for
> odd n geq 5 giving the limit superior 3/2; however, Konyagin and Browkin
> did not consider condition (3). The present work reports the following
> main results:
>
> (a) For odd n geq 5, the limit superior is at least 5/3;
>
> (b) For even n geq 6, the limit superior is at least 5/4.
>
> Furthermore, it is shown that for all n geq 6, one can disallow the members
> of the tuple to have any factor from a finite subset F of {3,4,5,...} and
> nevertheless obatin the limit superior 5/4. The last part of the talk reports
> on some analogous result for the Gaussian integers.
>
> Tianyu Liu is writing an UROP about verifying the main claims in the paper
> with the proof assistant COQ and it is planned to work this out to a second
> part of this publication.
>
> This is joint work of Aquinas Hobor, Rupert Hoelzl, Elaine Li, Tianyu Liu
> and Frank Stephan.
>
> Wikipedia Page: https://en.wikipedia.org/wiki/N_conjecture
>
> Paper: https://www.comp.nus.edu.sg/~fstephan/strongnconjecture.pdf
>
> Slides: https://www.comp.nus.edu.sg/~fstephan/strongnconjectureslides.pdf
>
> Seminar Webpage: https://www.comp.nus.edu.sg/~fstephan/logicseminar.html
>
Zoom Address for the Seminar Talk Next Week Wednesday (Logic Seminar NUS)
NUS Logic Seminar
3/27/2020 2:49:42
Dear participants,
The logic seminar will be held as a Zoom Meeting.
In the case that you want to join, please use the following
link on 1 April 2020 a bit before 17:00 hrs Singapore time:
https://nus-sg.zoom.us/j/138746532
Best regards, Frank Stephan
------------------------------------------------------------------------
Invitation to the Logic Seminar at the National University of Singapore
Date: Wednesday, 1 April 2020, 17:00 hrs (Singapore Time)
Room: S17#04-06, Department of Mathematics, NUS
Speaker: Frank Stephan
Title: Lower Bounds for the Strong N-Conjecture
Abstract:
The strong n-conjecture is a generalisation of the abc-conjecture
concerning the limit superior of qualities of n-tuples of integers which
(1) are pairwise co-prime;
(2) have the sum 0;
(3) do not have nontrivial subsums giving 0.
The quality of a tuple is the logarithm of the largest member (by absolute
value) divided by the logarithm of the largest square-free divider of the
product of all members of the tuple. Originally it was conjectured that
the limit superior of these qualities is 1, see the Wikipedia page at
https://en.wikipedia.org/wiki/N_conjecture
but Konyagin (as reported by Browkin 2000) found already an example for
odd n geq 5 giving the limit superior 3/2; however, Konyagin and Browkin
did not consider condition (3). The present work reports the following
main results:
(a) For odd n geq 5, the limit superior is at least 5/3;
(b) For even n geq 6, the limit superior is at least 5/4.
Furthermore, it is shown that for all n geq 6, one can disallow the members
of the tuple to have any factor from a finite subset F of {3,4,5,...} and
nevertheless obatin the limit superior 5/4. The last part of the talk reports
on some analogous result for the Gaussian integers.
Tianyu Liu is writing an UROP about verifying the main claims in the paper
with the proof assistant COQ and it is planned to work this out to a second
part of this publication.
This is joint work of Aquinas Hobor, Rupert Hoelzl, Elaine Li, Tianyu Liu
and Frank Stephan.
Wikipedia Page: https://en.wikipedia.org/wiki/N_conjecture
Paper: https://www.comp.nus.edu.sg/~fstephan/strongnconjecture.pdf
Slides: https://www.comp.nus.edu.sg/~fstephan/strongnconjectureslides.pdf
Seminar Webpage: https://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Logic Seminar Talk 1 April 2020 17:00 hrs at NUS
NUS Logic Seminar
3/27/2020 0:52:04
Invitation to the Logic Seminar at the National University of Singapore
Date: Wednesday, 1 April 2020, 17:00 hrs (Singapore Time)
Room: S17#04-06, Department of Mathematics, NUS
Speaker: Frank Stephan
Title: Lower Bounds for the Strong N-Conjecture
Abstract:
The strong n-conjecture is a generalisation of the abc-conjecture
concerning the limit superior of qualities of n-tuples of integers which
(1) are pairwise co-prime;
(2) have the sum 0;
(3) do not have nontrivial subsums giving 0.
The quality of a tuple is the logarithm of the largest member (by absolute
value) divided by the logarithm of the largest square-free divider of the
product of all members of the tuple. Originally it was conjectured that
the limit superior of these qualities is 1, see the Wikipedia page at
https://en.wikipedia.org/wiki/N_conjecture
but Konyagin (as reported by Browkin 2000) found already an example for
odd n geq 5 giving the limit superior 3/2; however, Konyagin and Browkin
did not consider condition 3. The present work reports the following
main results:
(a) For odd n geq 5, the limit superior is at least 5/3;
(b) For even n geq 6, the limit superior is at least 5/4.
Furthermore, it is shown that for all n geq 6, one can disallow the members
of the tuple to have any factor from a finite subset F of {3,4,5,...} and
nevertheless obatin the limit superior 5/4. The last part of the talk reports
on some analogous result for the Gaussian integers.
Tianyu Liu is writing an UROP about verifying the main claims in the paper
with the proof assistant COQ and it is planned to work this out to a second
part of this publication.
This is joint work of Aquinas Hobor, Rupert Hoelzl, Elaine Li, Tianyu Liu
and Frank Stephan.
Wikipedia Page: https://en.wikipedia.org/wiki/N_conjecture
Paper: https://www.comp.nus.edu.sg/~fstephan/strongnconjecture.pdf
Slides: https://www.comp.nus.edu.sg/~fstephan/strongnconjectureslides.pdf
Seminar Webpage: https://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Wednesday seminar
Prague Set Theory Seminar
3/26/2020 7:56:04
Dear all,
There is no seminar in Prague next week.
However, people are instead invited to participate the joint Jerusalem
and Bar Ilan set theory seminar which will take place on Wednesday April
1st as an online video conference via Zoom.
Program: Menachem Magidor will speak about the Friedman--Martin theorem
that Borel determinacy can not be proved in Zermelo Set Theory. Namely
one needs reflection for getting it.
The seminar is scheduled to start at 11:00 Israeli time (which should be
10:00 CEST according to my calculations).
The data to joint the video conference:
https://zoom.us/j/243676331
Zoom meeting ID: 243 676 331
Best,
David
Wednesday seminar
Prague Set Theory Seminar
3/23/2020 6:45:19
Dear all,
Because of the current quarantine situation, the Prague Wednesday
seminars are cancelled until further notice.
However, there will be an online seminar (zoom) on Wednesday March 25th
at 9:00--11:00 CET at the Bar-Ilan University, organized by Assaf Rinot.
Menachem Kojman -- Strong colorings over partitions
https://math.biu.ac.il/en/node/864
If you are interested in joining the seminar online, please contact
Assaf Rinot (or me).
Best,
David
Set Theory Seminar this week: Ming Xiao (important meeting information inside!)
Toronto Set Theory Seminar
3/16/2020 10:53:45
Hi everyone,
This week, Ming Xiao will give the seminar. His talk is entitled The Borel chain conditions.
Abstract: In this talk, I will present some examples of Borel posets and show that the hierarchy of partition conditions proposed by Horn and Tarski (

-finite chain condition,

-bounded chain condition, etc.), when requiring the pieces of partition to be Borel, is still distinct.
IMPORTANT: The seminar will be held remotely using the Zoom software during the usual time, Friday from 1:30 to 3:00 EDT. If you are interested in participating in the seminar and currently NOT a member of the mailing list (e.g., from Set Theory Talks) please send me an email to receive more information about how to join the meeting.
Stay safe,
Bill Chen
Wednesday seminar
Prague Set Theory Seminar
3/16/2020 3:25:18
Dear all,
There is no seminar this week (Wednesday March 18th) due to the quarantine.
The decision and announcement about the next seminar will be made/sent
in about a week.
Best,
David
Logic Seminar 18 March 2020 17:00 hrs at NUS
NUS Logic Seminar
3/14/2020 23:48:12
Invitation to the Logic Seminar at the National University of Singapore
Date: Wednesday, 18 March 2020, 17:00 hrs
Room: S17#04-06, Department of Mathematics, NUS
Speaker: Borisa Kuzeljevic.
Title: Cofinal types on the the second uncountable cardinal.
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
In the talk we will present some basic results about the Tukey
ordering of the class of all directed sets whose cofinality is the
second uncountable cardinal. We will isolate some basic directed sets
in this class, and then show which of them have immediate successors
in this ordering.
This is a joint work with Stevo Todorcevic.
This Week in Logic at CUNY
This Week in Logic at CUNY
3/12/2020 22:10:46
Hi everyone,
So far as we know, all seminars are on hiatus for an indefinite period, due to concerns about the covid-19 situation. Regular mailings of This Week in Logic are suspended for the time being, although special announcements will be sent as needed.
Take care of yourselves and each other,
Jonas
Set theory seminar this Friday: Jeffrey Bergfalk
Toronto Set Theory Seminar
3/11/2020 10:34:26
Hi everyone,
This week, Jeffrey Bergfalk from UNAM (Morelia) will speak on Definable (co)homology, topological rigidity, and problems of classification.
Abstract: We describe recent work, joint with Martino Lupini and Aristotelis Panagiotopoulos, at the interface of descriptive set theory and algebraic topology. This work begins with a consideration of the topologies arising naturally in the course of homology and cohomology computations. Our analysis of these topologies has two main benefits:
1. It affords us characterizations of the Borel complexity of several well-studied classification problems in mathematics, and
2. It yields refinements of classical homological and cohomological invariants which are valuable in their own right for the study of topological spaces.
We term the framework of these refined invariants definable (co)homology; this framework amounts to a retention of the descriptive set-theoretic information inhering in algebraic topology computations. These invariants are strong enough to imply several topological rigidity results concerning solenoids (of any dimension) and maps thereon. We will also show that techniques from algebraic topology can, reciprocally, extend the reach of descriptive set theory, by bounding, and in some cases precisely determining, the Borel complexity of classification problems concerning C*- algebras, their automorphisms, or Hermitian line bundles.
The talk will be held on Friday, March 13 in Fields 210 at 1:30 pm. If you will attend, please register using the following link:
Thanks,
Bill Chen
This Week in Logic at CUNY
This Week in Logic at CUNY
3/8/2020 22:09:13
This Week in Logic at CUNY:
- - - - Monday, Mar 9, 2020 - - - -
Logic and Metaphysics Workshop
Date: Monday, March 9, 4.15-6.15
Place: Room 7395, CUNY Graduate Center
Antonella Mallozzi (Providence College).
Title: Is There an Absolute Modality?
Abstract: Modality seems distinctively pluralistic: there are many kinds of possibility and necessity (logical, physical, metaphysical, normative, etc.), which seem significantly different from one another. However, the various modalities also seem to have much in common–perhaps simply in virtue of being kinds of modality. Should we suppose that there is some fundamental modality, one to which all the other modalities can be somehow reduced? Modal Monism says yes. Particularly, monists may treat the different modalities as relative to some absolute modality. However, Monism, reductionism, and absolute modality need not be a package. Specifically, the claim that some modality is absolute can be understood in ways which are independent of Monism and reductionism. In this talk, I raise concerns for monistic and reductionist programs in modal metaphysics, while also arguing that the notion of absolute modality is ambiguous. Depending on the framework, it means different things and captures quite different desiderata. After exploring several ways of disambiguating it, I suggest that while we possess and deploy a concept of absolute modality, that may be empty; or, otherwise put, no modal truth has the property of being “absolute”. I propose a pluralistic picture that still treats the different modalities as relative, while avoiding both absolute modality and reductionism. Importantly, the proposal won’t impact the philosophical significance of metaphysical modality.
- - - - Tuesday, Mar 10, 2020 - - - -
- - - - Wednesday, Mar 11, 2020 - - - -
The New York City Category Theory Seminar
Department of Computer Science, Department of Mathematics
The Graduate Center of The City University of New York
Speaker: Tai-Danae Bradley, The Graduate Center, CUNY.
Date and Time: Wednesday March 11, 2020, 7:00 - 8:30 PM., Room 6417.
Title: Modeling Probability Distributions as Quantum States.
Abstract: This talk features a passage from classical probability to quantum probability. The quantum version of a classical probability distribution is a density operator on a Hilbert space. The quantum version of a marginal probability distribution is a reduced density operator, and the operation that plays the role of marginalization is the partial trace. In particular, every joint probability distribution on a finite set can be modeling as a rank 1 density operator—a pure quantum state. With the partial trace, we recover the classical marginal probabilities, but we also uncover additional information. This extra information can be understood explicitly from the spectral information of the reduced density operators. I’ll describe these ideas and share how they contribute to understanding mathematical structure within natural language.
- - - - Thursday, Mar 12, 2020 - - - -
- - - - Friday, Mar 13, 2020 - - - -
Model Theory Seminar
CUNY Graduate Center, Room 6417
Friday, March 13, 12:30-2:00pm
Rebecca Coulson, United States Military Academy
TBA
Logic Workshop
CUNY Graduate Center, Room 6417
Friday, March 13, 2:00-3:30pm
Chris Conidis, CUNY
The complexity of radical constructions in rings and modules
We present two different elementary algebraic constructions that are as complicated as possible and whose complexity vastly exceeds those typically found in the elementary algebra literature. The first is the prime radical of a noncommutative ring, while the second is the radical of a module. These constructions contrast similar constructions in more familiar contexts that we will also mention along the way. We will spend most of our time describing how to construct radicals that are as complicated as possible from a computability point of view.
Next Week in Logic at CUNY:
- - - - Monday, Mar 16, 2020 - - - -
Logic and Metaphysics Workshop
Date: Monday, March 16, 4.15-6.15
Place: Room 7395, CUNY Graduate Center
David Papineau (CUNY)
Title: The Statistical Nature of Causation
Abstract: For over a hundred years econometricians, epidemiologists, educational sociologists and other non-experimental scientists have used asymmetric correlational patterns to infer directed causal structures. It is odd, to say the least, that no philosophical theories of causation cast any light on why these techniques work. Why do the directed causal structures line up with the asymmetric correlational patterns? Judea Pearl says that the correspondence is a “gift from the gods”. Metaphysics owes us a better answer. I shall attempt to sketch the outline of one.
- - - - Tuesday, Mar 17, 2020 - - - -
- - - - Wednesday, Mar 18, 2020 - - - -
- - - - Thursday, Mar 19, 2020 - - - -
- - - - Friday, Mar 20, 2020 - - - -
Ad Hoc Workshop on the Semantic Paradoxes
When? Friday March 20, Noon-5pm
Where? CUNY Graduate Center, room TBA
Who?
Will Nava, NYU, ‘Expressability and the (Un)Paradoxicality Paradoxes’
Brian Porter, GC, ‘Paraconsistent and Paracomplete Solutions to the Validity Curry Paradox’
Chris Scambler, NYU, ‘Metainferences and Paradox’
Open to? All interested
Queries? Graham Priest,
priest.graham@gmail.comThe workshop is sponsored by the Kripke Center.
- - - - Other Logic News - - - -
- - - - Web Site - - - -
Find us on the web at:
nylogic.github.io(site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to
jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email
jreitz@nylogic.org.
Logic Seminar Wed 11 March 2020 17:00 hrs at NUS by Thilo Weinert
NUS Logic Seminar
3/8/2020 18:24:12
Invitation to the Logic Seminar at the National University of Singapore
Date: Wednesday, 11 March 2020, 17:00 hrs
Room: S17#04-06, Department of Mathematics, NUS
Speaker: Thilo Weinert, NUS
Title: Polarised partition relation for order types
URL: https://arxiv.org/abs/1810.13316
and https://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Abstract:
We analyse partitions of products with two ordered factors in two
classes where both factors are countable or well-ordered and at least
one of them is countable. This relates the partition properties of
these products to cardinal characteristics of the continuum. We build
on work by Erdoes, Garti, Jones, Orr, Rado, Shelah and
Szemeredi. In particular, we show that a theorem of Jones
extends from the natural numbers to the rational ones but consistently
extends only to three further equimorphism classes of countable
orderings. This is made possible by applying a thirteen-year old
theorem of Orr about embedding a given order into a sum of finite
orders indexed over the given order.
This is joint work with Lukas Klausner
Fulgencio Lopez, Uncountable equilateral sets and anti-Ramsey families of functions.
IMPAN Working Group in Applications of Set Theory
3/7/2020 13:45:59
Seminar: Working group in applications of set theory, IMPAN
Tuesday, 10.03.2020, 10:15 pm, room 105, IMPAN, Śniadeckich 8, Warsaw.
Speaker: Fulgencio Lopez (IMPAN)
Title: "Uncountable equilateral sets and anti-Ramsey families of functions."
Abstact: "The study of equilateral and separated sets in Banach spaces has been an active area of interest since Petty considered this question in non euclidean spaces in 1971. We will give some background results in the area and then focus on the case of spaces of continuous functions. In particular we will show that having an anti-Ramsey family of functions implies there is a compact connected K, such that its space of continuous functions has no uncountable equilateral sets. A known result says that the existence of uncountable equilateral sets in all nonseparable C(K) spaces is undecidable." (joint work with P. Koszmider)
Visit our seminar webpage which may include announcements of some future talks at https://www.impan.pl/~set_theory/Seminar/
Cheers, Piotr.
Set theory seminar this Friday
Toronto Set Theory Seminar
3/4/2020 11:12:37
Hi everyone,
Hossein will speak in the seminar this week. His talk is entitled
Rigidity of Souslin trees and
.
Abstract:
We will show that

is consistent with the statement there is no minimal Souslin tree. This answers a question due to Baumgartner. We will also show that there is a Souslin tree

whose restriction on any

is rigid and forcing with

makes

a Kurepa tree. This answers a question due to Gunter Fuchs.
The talk will be held on Friday, March 6 in Fields 210 at 1:30 pm. The talk is expected to be short, probably less than an hour in duration. If you will attend, please register using the following link:
Thanks,
Bill Chen
This Week in Logic at CUNY
This Week in Logic at CUNY
3/1/2020 21:30:00
This Week in Logic at CUNY:
- - - - Monday, Mar 2, 2020 - - - -
Logic and Metaphysics Workshop
Date: Monday, March 2, 4.15-6.15
Place: Room 7395, CUNY Graduate Center
Alex Citkin (Metropolitan Telecommunications).
Title: Deductive Systems with Unified Multiple-Conclusion Rules
Abstract: Some people fight for the rights of animals, I am fighting for the rights of rejected propositions. Following the approach suggested by Brentano and accepted and developed by Lukasiewicz, I study the deductive systems that treat asserted and rejected propositions equally, in the same way. By “statement,” we understand the expressions of form +A – “A being asserted”, and -A$ – “A being rejected”, where A is a proposition. Accordingly, by a “unified logic,” we understand a consequence relation between sets of statements and statements. We introduce the unified deductive systems which can be used to define the unified logics. Unified deductive system consists of axioms, anti-axioms, and the multiple conclusion inference rules which premises and conclusions are the statements rather than the propositions. In particular, we study the deductive systems that contain the coherency rule, which means that one cannot assert and reject the same proposition at the same time, and the fullness rule, which means that each proposition is either asserted or rejected. Inclusion of these rules though does not enforce the law of excluded middle, or the law of non-contradiction on the propositional level.
- - - - Tuesday, Mar 3, 2020 - - - -
- - - - Wednesday, Mar 4, 2020 - - - -
The New York City Category Theory Seminar
Department of Computer Science, Department of Mathematics
The Graduate Center of The City University of New York
Speaker: Noah Chrein, University of Maryland.
Date and Time: Wednesday March 4, 2020, 7:00 - 8:30 PM., Room 6417.
Title: Hierarchy and Anisotropy in Categorical Ontology.
Abstract: The theory of sheaves on a site allows us to break down objects into local pieces and recover data about the global object. We wish to treat systems outside of mathematics in the same way: by breaking down objects into local pieces, analyzing the local pieces, and recombining to get an analysis of the whole. When running a simulation, it's not always relevant to understand the atoms of every object, sometimes it is enough to understand objects abstractly, this is the concept of "anisotropy". We propose a modeling scheme that follows the development of sheaf theory, and adds a notion of hierarchical anisotropy. Namely, instead of a covering in a site, {U_i -> X}, we will treat the U_i and X in two different categories, with "Ontological Expansions" O(X) = {U_i}. In this way, we can decide to treat objects globally, or if we need more specific information, we can expand into local pieces. To this end we define a Hierarchical Ontology.
- - - - Thursday, Mar 5, 2020 - - - -
- - - - Friday, Mar 6, 2020 - - - -
Model Theory Seminar
CUNY Graduate Center, Room 6417
Friday, March 6, 12:30-2:00pm
Dave Marker, McMaster University
Computability of the countable saturated differentially closed field
It's been known since work of Harrington in the early 1970s that computable differential fields have computable differential closures. Recently Calvert, Frolov, Harizanov, Knight, McCoy, Soskova, and Vatev showed that the countable saturated differentially closed field is computable. Their proof involves first creating an effective listing of all types and then using a result of Morley's on existence of computable saturated models. I will give a significant simplification of the enumeration result and, for completeness, sketch Morley's priority construction of a saturated model. Pillay has also given an alternative enumeration argument though ours seems more robust and generalizes to quantifier free types in ACFA.
Logic Workshop
CUNY Graduate Center, Room 6417
Friday, March 6, 2:00-3:30pm
Johanna Franklin, Hofstra University
Lowness for isomorphism and Turing degrees
A Turing degree is low for isomorphism if whenever it can compute an isomorphism between two countably presented structures, there is already a computable isomorphism between them and thus there is no need to use the degree as an oracle at all. I will discuss the types of degrees that are low for isomorphism and the extent to which this class of degrees has the same properties as other lowness classes.
This work is joint with Reed Solomon.
Next Week in Logic at CUNY:
- - - - Monday, Mar 9, 2020 - - - -
Logic and Metaphysics Workshop
Date: Monday, March 9, 4.15-6.15
Place: Room 7395, CUNY Graduate Center
Alex Citkin (Metropolitan Telecommunications).
Title: Deductive Systems with Unified Multiple-Conclusion Rules
Abstract: Some people fight for the rights of animals, I am fighting for the rights of rejected propositions. Following the approach suggested by Brentano and accepted and developed by Lukasiewicz, I study the deductive systems that treat asserted and rejected propositions equally, in the same way. By “statement,” we understand the expressions of form +A – “A being asserted”, and -A$ – “A being rejected”, where A is a proposition. Accordingly, by a “unified logic,” we understand a consequence relation between sets of statements and statements. We introduce the unified deductive systems which can be used to define the unified logics. Unified deductive system consists of axioms, anti-axioms, and the multiple conclusion inference rules which premises and conclusions are the statements rather than the propositions. In particular, we study the deductive systems that contain the coherency rule, which means that one cannot assert and reject the same proposition at the same time, and the fullness rule, which means that each proposition is either asserted or rejected. Inclusion of these rules though does not enforce the law of excluded middle, or the law of non-contradiction on the propositional level.
- - - - Tuesday, Mar 10, 2020 - - - -
- - - - Wednesday, Mar 11, 2020 - - - -
The New York City Category Theory Seminar
Department of Computer Science, Department of Mathematics
The Graduate Center of The City University of New York
Speaker: Tai-Danae Bradley, The Graduate Center, CUNY.
Date and Time: Wednesday March 11, 2020, 7:00 - 8:30 PM., Room 6417.
Title: Modeling Probability Distributions as Quantum States.
Abstract: This talk features a passage from classical probability to quantum probability. The quantum version of a classical probability distribution is a density operator on a Hilbert space. The quantum version of a marginal probability distribution is a reduced density operator, and the operation that plays the role of marginalization is the partial trace. In particular, every joint probability distribution on a finite set can be modeling as a rank 1 density operator—a pure quantum state. With the partial trace, we recover the classical marginal probabilities, but we also uncover additional information. This extra information can be understood explicitly from the spectral information of the reduced density operators. I’ll describe these ideas and share how they contribute to understanding mathematical structure within natural language.
- - - - Thursday, Mar 12, 2020 - - - -
- - - - Friday, Mar 13, 2020 - - - -
Logic Workshop
CUNY Graduate Center, Room 6417
Friday, March 13, 2:00-3:30pm
Chris Conidis, CUNY
TBA
- - - - Other Logic News - - - -
CONFERENCE ANNOUNCEMENT:
We are pleased to announce that the 2020 Boise Extravaganza in Set Theory (BEST) conference will take place in Ashland, Oregon, on the campus of Southern Oregon University, June 17–18, 2020.
https://www.boisestate.edu/math/best/ BEST is an international conference featuring talks on a broad range of recent advances in research in set theory, logic, and related fields. Researchers from all areas of set theory and logic are welcome. BEST particularly aims to support the careers of young researchers. The conference is organized by the Set Theory and Logic group at Boise State University and is structured as a symposium of the annual meeting of the AAAS, Pacific Division.
- - - - Web Site - - - -
Find us on the web at:
nylogic.github.io(site designed, built & maintained by Victoria Gitman)
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Wednesday seminar
Prague Set Theory Seminar
2/29/2020 10:58:52
Dear all,
There will be no seminar on Wednesday for the next two weeks (regular
participants are unavailable). The seminar should meet again on
Wednesday March 18th.
Best,
David
Tomasz Kochanek, On representations of the Calkin algebra - the noncommutative analogue of P(N)/Fin or l∞/c0 II
IMPAN Working Group in Applications of Set Theory
2/29/2020 9:01:08
Seminar: Working group in applications of set theory, IMPAN
TUESDAY, 3.03.2020,
Seminar at 10:15 pm, room 105, IMPAN, Śniadeckich 8, Warsaw.
Speaker: Tomasz Kochanek (IM PAN/MIM UW)
Title: " On representations of the Calkin algebra - the noncommutative analogue of P(N)/Fin or l∞/c0 II "
Abstact: "Continuing our study of the poset of projections of the Calkin algebra Q(H), we will first show that below any strictly decreasing sequence of projections of Q(H) there is some nonzero projection. This fact gives rise to considering a `quantized` analogue of the pseudointersection number. Next, we will prove a general result saying that the poset of projections of Q(A) does not form a lattice, whenever Q(A) is the corona algebra of any stabilization A of some unital C*-algebra. In particular, this implies that the Calkin algebra is not an AW*-algebra. Then, we will proceed to the problem of representation of Q(H), focusing on two papers. First, Anderson and Bunce (Amer. J. Math. 1977) showed that under Martin's axiom (as well as under the Continuum Hypothesis), there exists a faithful *-representation of Q(H) such that the WOT-closure of its range is a II∞ type factor. Later, Anderson (J. Funct. Anal. 1979) showed that such a result holds true in ZFC. We shall discuss both of those (quite similar) constructions.".
Visit our seminar webpage which may include announcements of some future talks at https://www.impan.pl/~set_theory/Seminar/
Cheers, Piotr.
(KGRC) research seminar talk on Thursday, March 5
Kurt Godel Research Center
2/27/2020 15:32:02
The KGRC welcomes as guests:
Jana Marikova (host: Benjamin Miller) will stay until June 30.
Clifton Ealy (host: Benjamin Miller) will visit from March 7 to March 15 and
from May 9 to June 30.
Miguel Moreno (host: Lyubomyr Zdomskyy) will stay until November 30 and give a
talk on January 23.
Jerzy Kakol (host: Damian Sobota) will stay from March 29 to April 4 and give a
talk on April 2.
Chi Tat Chong (host: Sy-David Friedman) will stay from June 17 to June 19 and
give a talk on June 18.
(Note: Professor Zeman's visit in the first week of March had to be canceled.)
* * *
Research seminar
Kurt Gödel Research Center
Thursday, March 5
"$\Pi_1^1$-subcompactness and type omission"
Yair Hayut (KGRC)
Strongly compact cardinals can be characterized in various ways: compactness of
$L_{\kappa,\kappa}$, filter extensions, the existence of fine measures, the
strong tree property (+inaccessibility) and many other ways. Localizations of
those definitions produce a rich hierarchy. Supercompact cardinals have much
fewer parallel characterizations, obtained typically by adding a normality
assumption.
In this talk I will present a characterization of supercompact cardinals in
terms of compactness of $L_{\kappa,\kappa}$ with type omission. Using it, I
will present a variant of the strong tree property which is (locally) weaker
than the ineffable tree property and together with inaccessibility characterize
supercompactness. Those characterizations localize to a characterization of
$\Pi^1_1$-subcomapctness.
This is a joint work with Menachem Magidor.
Time and Place
Tea at 3:30pm in the KGRC meeting room (seminar room CST5.47)
Talk at 4:00pm in the KGRC lecture room (seminar room D5.48)
Universität Wien
Institut für Mathematik
Kurt Gödel Research Center
Augasse 2-6, UZA 1 - Building 2
1090 Wien
Set Theory Seminar this Friday
Toronto Set Theory Seminar
2/26/2020 11:38:54
We will continue with the second part of the talk this Friday, February 28 in Fields 210 from 1:30 to 3:00. If you will attend the talk, please register using the following link:
Bill Chen
Hi everyone,
I will talk this week about selectivity properties of spaces.
Abstract: This talk addresses several questions of Feng, Gruenhage, and Shen which arose from Michael's theory of continuous selections from countable spaces. This theory is concerned with the following general question about topological spaces: when does a map from

into the hyperspace of closed nonempty subsets of

admit a continuous selection

?
We construct a space which is

-selective but not

-selective from

, and an

-selective space which is not selective for a

-point ultrafilter from CH. We also produce ZFC examples of Fréchet spaces where countable subsets are first countable which are not

-selective. All of the notions will be defined in the talk, joint work with Paul Szeptycki.
The talk will be held at the usual time and place on Friday, February 14 in Fields 210 from 1:30 to 3:00. If you will attend the talk, please register using the following link:
Thanks,
Bill Chen
Fernando Javier Núñez Rosales: Teoría descriptiva de grupos polacos no arquimedianos de transformaciones
Mexico City Logic Seminar
2/25/2020 11:52:00
Los grupos polacos no arquimedianos se pueden realizar como grupos de automorfismos de estructuras de Fraïssé. El objetivo de esta plática es revisar algunos fenómenos de la dinámica de estos grupos, los cuales pueden ser estudiados a través de propiedades combinatorias de clases de estructuras finitas o sistemas asociados a estas vía teoría de Fraïssé. Algunos de los tópicos centrales serán la extrema promediabilidad; el cómputo de flujos minimales universales; la existencia de simetrías genéricas y de genéricos enormes; aproximación por compactos; turbulencia; entre otras. Estos tópicos serán ilustrados con ejemplos.
Tagged: Fernando Javier Núñez Rosales
Logic Seminar 4 March 2020 17:00 hrs at NUS by Andre Nies
NUS Logic Seminar
2/24/2020 21:20:21
Invitation to the Logic Seminar at the National University of Singapore
Date: Wednesday, 4 March 2019, 17:00 hrs
Room: S17#04-06, Department of Mathematics, NUS
Speaker: Andre Nies, University of Auckland
Title: Analogs of combinatorial cardinal characteristics in
computability theory
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Abstract:
Our basic objects are infinite sets of natural numbers. In set theory,
the MAD number is the least cardinality of a maximal almost disjoint
class of sets of natural numbers. The ultrafilter number is the least
size of an ultrafilter base.
We study computability theoretic analogs of these cardinals. In our
approach, all the basic objects will be infinite computable sets. A
class of such basic objects is encoded as the set of columns of a set
R, which allows us to study the Turing complexity of the class.
We show that each non-low oracle computes a MAD class R, give a
finitary construction of a c.e. MAD set (compatible with permitting),
and on the other hand show that a 1-generic below the halting problem
does not compute a MAD class.
We show that the Turing degrees of ultrafilter bases are precisely the
high degrees.
Joint work with: Steffen Lempp, Joseph S. Miller and Mariya Soskova
Reference: Section 8 of Logic Blog 2019 on Andre's homepage; soon also
available as technical report on http://www.arxiv.org/.
SPECIAL ANNOUNCEMENT - This Week in Logic at CUNY - Two add'l talks today
This Week in Logic at CUNY
2/24/2020 12:35:59
Hi everyone,
Please see the announcement below, provided by Dennis Sullivan.
Best,
Jonas
---------------------------------
Prof. Francisco Javier Torres de Lizaur from Spain will give two talks today at the Einstein Chair seminar today, February 24, 2020:
The first will relate to geometry.
The second will relate to 3D fluid solutions in space to logic, computer science and PDE.
Namely, at 4:00p in logic knowing if a point enters a region contains the halting problem.
This affects PDE, analysis and computer science and at 2:00p finding links knots and foliations in stationary solutions of Euler’s fluid PDE in 3D.
<2:00p to tea then 4:00 to 5:00p>
<ROOM 6417>
This Week in Logic at CUNY
This Week in Logic at CUNY
2/23/2020 20:33:37
This Week in Logic at CUNY:
- - - - Monday, Feb 24, 2020 - - - -
Logic and Metaphysics Workshop
Date: Monday, February 24, 4.15-6.15
Place: Room 7395, CUNY Graduate Center
Dongwoo Kim (CUNY)
Title: A Truthmaker Semantics for Modal Logics
Abstract: This paper attempts to provide an exact truthmaker semantics for a family of normal modal propositional logic. The new semantics can be regarded as an “exactification” of the Kripke semantics in the sense of Fine (2014). For it offers an account of the accessibility relation on worlds in terms of the banning and allowing relations on states. The main idea is that an exact truthmaker for “Necessarily P” is a state that bans the exact falsifiers of P from obtaining, and an exact truthmaker for “Possibly P” is a state that allows the exact verifiers of P to obtain.
- - - - Tuesday, Feb 25, 2020 - - - -
- - - - Wednesday, Feb 26, 2020 - - - -
The New York City Category Theory Seminar
Department of Computer Science, Department of Mathematics
The Graduate Center of The City University of New York
Speaker: Noson S. Yanofsky, Brooklyn College, CUNY.
Date and Time: Wednesday February 26, 2020, 7:00 - 8:30 PM., Room 6417.
Title: Higher-Order Categorical Logic: From Section 1.7 and on.
Abstract: We will be talking about Polynomial categories and Kleisli categories of cotriples. We will also talk about coproducts in Cartesian closed categories and natural number objects.
- - - - Thursday, Feb 27, 2020 - - - -
- - - - Friday, Feb 28, 2020 - - - -
Logic Workshop
CUNY Graduate Center, Room 6417
Friday, February 28, 2:00-3:30pm
Joel Nagloo, CUNY
TBA
Next Week in Logic at CUNY:
- - - - Monday, Mar 2, 2020 - - - -
Logic and Metaphysics Workshop
Date: Monday, March 2, 4.15-6.15
Place: Room 7395, CUNY Graduate Center
Alex Citkin (Metropolitan Telecommunications).
Title: Deductive Systems with Unified Multiple-Conclusion Rules
Abstract: Some people fight for the rights of animals, I am fighting for the rights of rejected propositions. Following the approach suggested by Brentano and accepted and developed by Lukasiewicz, I study the deductive systems that treat asserted and rejected propositions equally, in the same way. By “statement,” we understand the expressions of form +A – “A being asserted”, and -A$ – “A being rejected”, where A is a proposition. Accordingly, by a “unified logic,” we understand a consequence relation between sets of statements and statements. We introduce the unified deductive systems which can be used to define the unified logics. Unified deductive system consists of axioms, anti-axioms, and the multiple conclusion inference rules which premises and conclusions are the statements rather than the propositions. In particular, we study the deductive systems that contain the coherency rule, which means that one cannot assert and reject the same proposition at the same time, and the fullness rule, which means that each proposition is either asserted or rejected. Inclusion of these rules though does not enforce the law of excluded middle, or the law of non-contradiction on the propositional level.
- - - - Tuesday, Mar 3, 2020 - - - -
- - - - Wednesday, Mar 4, 2020 - - - -
The New York City Category Theory Seminar
Department of Computer Science, Department of Mathematics
The Graduate Center of The City University of New York
Speaker: Noah Chrein, University of Maryland.
Date and Time: Wednesday March 4, 2020, 7:00 - 8:30 PM., Room 6417.
Title: Hierarchy and Anisotropy in Categorical Ontology.
Abstract: The theory of sheaves on a site allows us to break down objects into local pieces and recover data about the global object. We wish to treat systems outside of mathematics in the same way: by breaking down objects into local pieces, analyzing the local pieces, and recombining to get an analysis of the whole. When running a simulation, it's not always relevant to understand the atoms of every object, sometimes it is enough to understand objects abstractly, this is the concept of "anisotropy". We propose a modeling scheme that follows the development of sheaf theory, and adds a notion of hierarchical anisotropy. Namely, instead of a covering in a site, {U_i -> X}, we will treat the U_i and X in two different categories, with "Ontological Expansions" O(X) = {U_i}. In this way, we can decide to treat objects globally, or if we need more specific information, we can expand into local pieces. To this end we define a Hierarchical Ontology.
- - - - Thursday, Mar 5, 2020 - - - -
- - - - Friday, Mar 6, 2020 - - - -
Logic Workshop
CUNY Graduate Center, Room 6417
Friday, March 6, 2:00-3:30pm
Johanna Franklin, Hofstra University
Lowness for isomorphism and Turing degrees
A Turing degree is low for isomorphism if whenever it can compute an isomorphism between two countably presented structures, there is already a computable isomorphism between them and thus there is no need to use the degree as an oracle at all. I will discuss the types of degrees that are low for isomorphism and the extent to which this class of degrees has the same properties as other lowness classes.
This work is joint with Reed Solomon.
- - - - Other Logic News - - - -
CONFERENCE ANNOUNCEMENT:
We are pleased to announce that the 2020 Boise Extravaganza in Set Theory (BEST) conference will take place in Ashland, Oregon, on the campus of Southern Oregon University, June 17–18, 2020.
https://www.boisestate.edu/math/best/ BEST is an international conference featuring talks on a broad range of recent advances in research in set theory, logic, and related fields. Researchers from all areas of set theory and logic are welcome. BEST particularly aims to support the careers of young researchers. The conference is organized by the Set Theory and Logic group at Boise State University and is structured as a symposium of the annual meeting of the AAAS, Pacific Division.
- - - - Web Site - - - -
Find us on the web at:
nylogic.github.io(site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to
jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email
jreitz@nylogic.org.
Tomasz Kochanek, On representations of the Calkin algebra - the noncommutative analogue of P(N)/Fin or l∞/c0
IMPAN Working Group in Applications of Set Theory
2/22/2020 9:39:21
Seminar: Working group in applications of set theory, IMPAN
Note the change from Thursdays to Tuesdays and afternoons to mornings.
TUESDAY, 25.02.2020,
Seminar at 10:15 pm, room 105, IMPAN, Śniadeckich 8, Warsaw.
Speaker: Tomasz Kochanek (IM PAN/MIM UW)
Title: " On representations of the Calkin algebra - the noncommutative analogue of P(N)/Fin or l∞/c0"
Abstact: "The first part will be a mild introduction to the Calkin algebra Q(H) which was first investigated thoroughly by J.W. Calkin in his paper published in Annals Math. in 1941. We shall present some basic facts on Q(H), explaining what it has to do with essential spectra, Fredholm operators, the BDF theory of extensions, and a few other things. With the aid of Banach limit, we will construct a `concrete' representation ρ of Q(H) on a Hilbert space of density continuum. Also, we will show that the range of ρ is not closed in the weak operator topology, which should provoke considering the problem of finding some `special' representations of Q(H), as well as the problem of extending *-homomorphisms into Q(H). This will be the topic of the second part".
Visit our seminar webpage which may include announcements of some future talks at https://www.impan.pl/~set_theory/Seminar/
Cheers, Piotr.
Wednesday seminar
Prague Set Theory Seminar
2/21/2020 12:39:39
Dear all,
The seminar meets on Wednesday February 26th at 11:00 in the Institute
of Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.
Program: Egbert Thümmel will talk about the non-existence of ω1 purely
injective ideals in Boolean algebras.
Best,
David
This Week in Logic at CUNY
This Week in Logic at CUNY
2/18/2020 22:30:32
This Week in Logic at CUNY:
- - - - Monday, Feb 17, 2020 - - - -
- - - - Tuesday, Feb 18, 2020 - - - -
- - - - Wednesday, Feb 19, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center, Room 4213.03 (Math Thesis Room)
Wednesday, February 19, 6:30-8:00pm
James Geiser
Soundness and the Gödel Undecidability Theorem
The goal of Gödel’s argument that the theory (T) of Peano Arithmetic is not complete, was to show that the Gödel sentences, GG , and it’s negation, are not provable in T, unless T is inconsistent. In this paper we examine the first half of this argument, namely, that from a hypothetical derivation, PGPG, of GG, a derivation, PfPf, can be constructed that ends in a contradiction. We make the observation that the Gödel argument depends on the metatheory concept of representability that, in turn, depends on the metatheory concept of soundness. Our analysis leads to two main observations, the first well know, and the second, a challenge to the standard undecidability argument.
1 – The existence of PGPG implies that T is unsound. This conclusion does not require the further construction, from PGPG, of the derivation PfPf.
2 - We argue that effectuation of the construction of PfPf is obstructed, because that effectuation requires acceptance of a contradiction in the metatheory regarding the soundness of T.
This is joint work with Catherine Hennix.
The New York City Category Theory Seminar
Department of Computer Science, Department of Mathematics
The Graduate Center of The City University of New York
Date and Time: Wednesday February 19, 2020, 7:00 - 8:30 PM., Room 6417.
Speaker: Todd Trimble, Western Connecticut State University.
Title: The Universal Property of the Bar Construction.
Abstract: The bar construction is a fundamental construction used throughout homological algebra and algebraic topology, including for example the construction of classifying bundles, deloopings of suitable H-spaces, and free resolutions of general algebras and the cohomology thereof. The underlying theme is that the bar construction produces canonical contractible or acyclic simplicial algebras, as usually explained by the acyclic models theorem. In this talk we sharpen this result, giving a precise sense in which the bar construction is a universal acyclic simplicial algebra, here recasting "acyclic" not as a property but as an algebraic structure, whereby acyclic structures are coalgebras over the decalage comonad.
- - - - Thursday, Feb 20, 2020 - - - -
- - - - Friday, Feb 21, 2020 - - - -
Logic Workshop
CUNY Graduate Center, Room 6417
Friday, February 21, 2:00-3:30pm
Andrey Morozov, Novosibirsk State UniversityOn ΣΣ-preorderings in HF(R)We prove that ω1ω1 cannot be embedded into any preordering ΣΣ-definable with parameters in the hereditarily finite superstructure over the ordered field of real numbers, HF(R). As corollaries, we obtain characterizations of ΣΣ-presentable ordinals and Gödel constructive sets of kind LαLα. It also follows that there are no ΣΣ-presentations for structures of TT-, mm-, 11-, and tttt-degrees over HF(R).
Next Week in Logic at CUNY:
- - - - Monday, Feb 24, 2020 - - - -
Logic and Metaphysics Workshop
Date: Monday, February 24, 4.15-6.15
Place: Room 7395, CUNY Graduate Center
Dongwoo Kim (CUNY)
Title: A Truthmaker Semantics for Modal Logics
Abstract: This paper attempts to provide an exact truthmaker semantics for a family of normal modal propositional logic. The new semantics can be regarded as an “exactification” of the Kripke semantics in the sense of Fine (2014). For it offers an account of the accessibility relation on worlds in terms of the banning and allowing relations on states. The main idea is that an exact truthmaker for “Necessarily P” is a state that bans the exact falsifiers of P from obtaining, and an exact truthmaker for “Possibly P” is a state that allows the exact verifiers of P to obtain.
- - - - Tuesday, Feb 25, 2020 - - - -
- - - - Wednesday, Feb 26, 2020 - - - -
The New York City Category Theory Seminar
Department of Computer Science, Department of Mathematics
The Graduate Center of The City University of New York
Date and Time: Wednesday February 26, 2020, 7:00 - 8:30 PM., Room 6417.
Title: Higher-Order Categorical Logic: From Section 1.7 and on.
Abstract: We will be talking about Polynomial categories and Kleisli categories of cotriples. We will also talk about coproducts in Cartesian closed categories and natural number objects.
- - - - Thursday, Feb 27, 2020 - - - -
- - - - Friday, Feb 28, 2020 - - - -
Logic Workshop
CUNY Graduate Center, Room 6417
Friday, February 28, 2:00-3:30pm
Joel Nagloo, CUNY
TBA
- - - - Other Logic News - - - -
CONFERENCE ANNOUNCEMENT:
We are pleased to announce that the 2020 Boise Extravaganza in Set Theory (BEST) conference will take place in Ashland, Oregon, on the campus of Southern Oregon University, June 17–18, 2020.
https://www.boisestate.edu/math/best/ BEST is an international conference featuring talks on a broad range of recent advances in research in set theory, logic, and related fields. Researchers from all areas of set theory and logic are welcome. BEST particularly aims to support the careers of young researchers. The conference is organized by the Set Theory and Logic group at Boise State University and is structured as a symposium of the annual meeting of the AAAS, Pacific Division.
- - - - Web Site - - - -
Find us on the web at:
nylogic.github.io(site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to
jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email
jreitz@nylogic.org.
Logic seminar this week cancelled
NUS Logic Seminar
2/18/2020 1:36:05
Hello,
I just want to inform you that our speaker for the logic seminar this
week is ill and on mc until Thursday. Therefore there is no logic seminar
this week. My apologies and all the best wishes to Thilo for his health.
Best regards, Frank
Wednesday seminar
Prague Set Theory Seminar
2/13/2020 6:13:04
Dear all,
There is no seminar next week, Wednesday February 19th.
The seminar should meet again on Wednesday February 26th.
Best,
David
Logic Seminar 19 Feb 2020 17:00 hrs at NUS
NUS Logic Seminar
2/13/2020 2:47:21
Invitation to the Logic Seminar at the National University of Singapore
Date: Wednesday, 19 February 2019, 17:00 hrs
Room: S17#04-06, Department of Mathematics, NUS
Speaker: Thilo Weinert, NUS
Title: Polarised partition relation for order types
URL: https://arxiv.org/abs/1810.13316
and https://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Abstract:
We analyse partitions of products with two ordered factors in two
classes where both factors are countable or well-ordered and at least
one of them is countable. This relates the partition properties of
these products to cardinal characteristics of the continuum. We build
on work by Erdoes, Garti, Jones, Orr, Rado, Shelah and
Szemeredi. In particular, we show that a theorem of Jones
extends from the natural numbers to the rational ones but consistently
extends only to three further equimorphism classes of countable
orderings. This is made possible by applying a thirteen-year old
theorem of Orr about embedding a given order into a sum of finite
orders indexed over the given order.
This is joint work with Lukas Klausner
Set Theory Seminar this Friday
Toronto Set Theory Seminar
2/12/2020 10:00:00
Hi everyone,
I will talk this week about selectivity properties of spaces.
Abstract: This talk addresses several questions of Feng, Gruenhage, and Shen which arose from Michael's theory of continuous selections from countable spaces. This theory is concerned with the following general question about topological spaces: when does a map from

into the hyperspace of closed nonempty subsets of

admit a continuous selection

?
We construct a space which is

-selective but not

-selective from

, and an

-selective space which is not selective for a

-point ultrafilter from CH. We also produce ZFC examples of Fréchet spaces where countable subsets are first countable which are not

-selective. All of the notions will be defined in the talk, joint work with Paul Szeptycki.
The talk will be held at the usual time and place on Friday, February 14 in Fields 210 from 1:30 to 3:00. If you will attend the talk, please register using the following link:
Thanks,
Bill Chen
Boise Extravaganza in Set Theory, Ashland, OR, June 17-18, 2020
Conference
2/12
We are pleased to announce that the 2020 Boise Extravaganza in Set Theory will take place in Ashland, Oregon, on the campus of Southern Oregon University, during June 17–18.
BEST is an international conference featuring talks on a broad range of recent advances in research in set theory and related fields. Researchers from all areas of logic are welcome. BEST particularly aims to support the careers of young researchers in set theory and logic. The conference is organized by the Set Theory group at Boise State University and is structured as a symposium of the annual meeting of the AAAS, Pacific Division.
Site: https://www.boisestate.edu/math/best/
Contact: best@boisestate.edu
Organizers: Liljana Babinkostova (Boise State University), John Clemens (Boise State University), Samuel Coskey (Boise State University), Marion Scheepers (Boise State University) Scientific support Natasha Dobrinen (University of Denver)
Plenary speakers:
* David Fernández-Bretón (Universidad Nacional Autónoma de México)
* Victoria Gitman (CUNY Graduate Center)
* Jun Le Goh (University of Wisconsin)
* Lynne Yengulalp (University of Dayton and Wake Forest University)
* Joseph Zielinski
* … more to come!
The NSF supports travel grants for student and postdoctoral speakers at BEST. (If you are in another category and could use funding, let us know as well.) We strongly encourage members of groups underrepresented in mathematics to apply! Please visit the conference web site for application instructions.
Tagged: David Fernández-Bretón, Jun Le Goh, Lynne Yengulalp, Joseph Zielinski, Victoria Gitman
Ultrafilters and Ultraproducts Across Mathematics, Pisa, Italy, May 31-June 6, 2020
Conference
2/11/2020
ULTRAMATH 2020
Ultrafilters and Ultraproducts Across Mathematics and Related Topics
May 31 - June 6, 2020, Pisa, Italy
http://people.dm.unipi.it/ultramath2020/
Dear all,
We are happy to announce the upcoming event "ULTRAMATH 2020 - Ultrafilters and Ultraproducts Across Mathematics and Related Topics", that will be held in Pisa (Italy) from May 31st to June 6th 2020.
The international Conference "ULTRAMATH 2020” aims to present recent results in the whole spectrum of mathematics which are grounded on the use of ultrafilters and ultraproducts.
Its main goals:
• Disseminate information about the various techniques related to the use of ultrafilters and ultraproducts, and their potential to attack open problems.
• Bring together researchers with different backgrounds, and encourage their collaborations and interactions, especially on topics connecting different areas of mathematics.
The covered topics of UltraMath 2020 include (but are not limited to):
• Additive and Combinatorial Number Theory.
• Combinatorics and Ramsey Theory.
• Algebra and Geometry.
• General Topology.
• Measure Theory.
• Ergodic Theory and Dynamics.
• Functional Analysis and Metric Spaces.
• Nonstandard Analysis and Model Theory.
• Generalized Spaces and Differential Equations.
• Set Theory.
Greater prominence will be given to those results that satisfy (most of) the following conditions:
• The results can be formulated and presented in non-specialist terms, and be in principle understandable by any practicing mathematician.
• The usage of ultrafilters/ultraproducts is important (or even essential) in obtaining these results.
• The results connect different areas of mathematics.
• The results reveal new facets of known important topics.
This is the second edition of “UltraMath”, after the one held in Pisa in 2008: http://people.dm.unipi.it/ultramath.
Scientific Committee:
Vitaly Bergelson (Ohio State University, USA)
Andreas Blass (University of Michigan, USA)
Mauro Di Nasso (Università di Pisa, Italia)
Renling Jin (College of Charleston, USA)
Organizing Committee:
Mauro Di Nasso (Università di Pisa, Italia) – chair
Lorenzo Luperi Baglini (Università di Milano, Italia)
LIST OF INVITED SPEAKERS
Vieri Benci — Università di Pisa, Italia
Vitaly Bergelson — Ohio State University, USA
Andreas Blass — University of Michigan Ann Arbor, USA
Artem Chernikov — University of California Los Angeles (UCLA), USA
Natasha Dobrinen — University of Denver, USA
Cornelia Druţu — University of Oxford, UK
Victoria Gitman — City University of New York (CUNY), USA
Isaac Goldbring — University of California Irvine (UCI), USA
C. Ward Henson – University of Illinois Urbana-Champaign, USA
Neil Hindman — Howard University, USA
Michael Hrušák — Universidad Nacional Autónoma, México
Renling Jin — College of Charleston, USA
Steven Leth — University of Northern Colorado, USA
Martino Lupini — Victoria University, New Zealand
Joel Moreira — University of Warwick, UK
Jaroslav Nešetřil — Charles University Praha, Czech Republic
Florian Richter – Northwestern University, USA
David A. Ross — University of Hawaii, USA
Sławomir Solecki — Cornell University, USA
Dona Strauss — University of Hull, UK
Simon Thomas — Rutgers University, USA
Stevo Todorcevic — Univ. of Toronto, Canada and Univ. Paris Diderot, France
There will be a call for contributed papers. Moreover, depending on the funds available, participation of young researchers and researchers from disadvantages areas will be supported.
You can preregister by sending an email to ultramath2020@cs.dm.unipi.it with your name and institution.
Updated information about UltraMath 2020 will be posted on the website: http://people.dm.unipi.it/ultramath2020/.
Those who need more information, can contact the organizers at: ultramath2020@cs.dm.unipi.it.
We hope to see you in Pisa!
Best regards,
The Organizers
Tagged: Vieri Benci, Vitaly Bergelson, Andreas Blass, Artem Chernikov, Natasha Dobrinen, Cornelia Druţu, Victoria Gitman, Isaac Goldbring, C. Ward Henson, Neil Hindman, Michael Hrušák, Renling Jin, Steven Leth, Martino Lupini, Joel Moreira, Jaroslav Nešetřil, Florian Richter, David A. Ross, Sławomir Solecki, Dona Strauss, Simon Thomas, Stevo Todorcevic
Logic Colloquium, Poznań, Poladn, July 13-18, 2020
Conference
2/10/2020
Logic Colloquium 2020
Call for Papers
July 13-18, 2020, Poznań, Poland
https://lc2020.pl/
* The Logic Colloquium is the European Summer Meeting of the Association for Symbolic Logic, which in 2020 will be
held from 13th to 18th of July at the Adam Mickiewicz University, Poznań, Poland. It is organized jointly by the
AMU Faculties: of Psychology and Cognitive Science and of Mathematics and Computer Science.
* Registration is now open.
* Important dates:
- March 31st, 2020 deadline for abstract submission
- April 13th, 2020 deadline for student travel awards applications
- April 30th, 2020 notifications
- May 25th, 2020 camera-ready abstracts due
- June 13th, 2020 early payments deadline
- July 7th, 2020 late payments deadline
* Goedel Lecture: Elisabeth Bouscaren (CNRS - Université Paris-Sud)
* Tutorial Speakers: Krzysztof Krupiński (University of Wrocław), Andrew Marks (University of California Los Angeles)
* Plenary Speakers: Linda Westrick (Pennsylvania State University), Benoit Monin (Créteil University), Noam Greenberg
(Victoria University of Wellington), Vera Fischer (University of Viena), Luca Motto Ros (University of Turin),
Elaine Pimentel (Federal University of Rio Grande do Norte), Frank Pfenning (Carnegie Mellon University),
Johan van Benthem (University of Amsterdam), Ryan Williams (Massachusetts Institute of Technology),
Artem Chernikov (University of California Los Angeles)
* Detailed information can be found on the webpage.
Tagged: Elisabeth Bouscaren, Krzysztof Krupiński, Andrew Marks, Linda Westrick, Benoit Monin, Noam Greenberg, Vera Fischer, Luca Motto Ros, Elaine Pimentel, Frank Pfenning, Johan van Benthem, Ryan Williams, Artem Chernikov
This Week in Logic at CUNY
This Week in Logic at CUNY
2/9/2020
This Week in Logic at CUNY:
- - - - Monday, Feb 10, 2020 - - - -
Logic and Metaphysics Workshop
Date: Monday, February 10, 4.15-6.15
Place: Room 7395, CUNY Graduate Center
Melissa Fusco (Columbia)
Is Free Choice Cancellable?
I explore the implications of the Tense Phrase deletion operation known as sluicing (Ross 1969) for the semantic and pragmatic literature on the Free Choice effect (Kamp 1973, von Wright 1969). I argue that the time-honored ‘I don’t know which’-riders on Free Choice sentences, traditionally taken to show that the effect is pragmatic, are sensitive to scope. Careful attention to such riders suggests that these sluices do not show cancellation on Free Choice antecedents in which disjunction scopes narrower than the modal.
- - - - Tuesday, Feb 11, 2020 - - - -
- - - - Wednesday, Feb 12, 2020 - - - -
NO TALKS TODAY - LINCOLN'S BIRTHDAY
Today's New York City Category Theory Seminar talk by Tai-Danae Bradley has been rescheduled for March 11.
- - - - Thursday, Feb 13, 2020 - - - -
- - - - Friday, Feb 14, 2020 - - - -
Logic Workshop
CUNY Graduate Center, Room 6417
Friday, February 14, 2:00-3:30pm
Bartosz Wcisło, University of Warsaw
Tarski boundary
Our talk concerns axiomatic theories of truth predicates. They are theories obtained by adding to Peano Arithmetic (PAPA) a fresh predicate T(x)T(x) with the intended reading 'xx is (a code of) a true sentence in the language of arithmetic' together with some axioms governing newly added predicate.
The canonical example of such a theory is CT−CT− (Compositional Truth). Its axioms state that the truth predicate is compositional. For instance, a conjunction is true iff both conjuncts are. If we add to CT−CT− full induction in the extended language, we call the resulting theory CTCT.
It is easy to check that CTCT is not conservative over PAPA, i.e., it proves new arithmetical sentences. On the other hand, by a nontrivial theorem of Kotlarski, Krajewski, and Lachlan, CT−CT− extends PAPA conservatively.
In our talk, we will discuss results on the strength of theories between CT−CT− and CTCT. It turns out that the natural axioms concerning purely truth theoretic properties of the newly added predicate (as opposed to axiom schemes which are consequences of induction in more general context) are typically either conservative or exactly equal to CT0CT0, the theory of compositional truth with Δ0Δ0-induction. Thus CT0CT0 turns out to be a surprisingly robust theory and, arguably, the minimal 'natural' non-conservative theory of truth.
Next Week in Logic at CUNY:
- - - - Monday, Feb 17, 2020 - - - -
- - - - Tuesday, Feb 18, 2020 - - - -
- - - - Wednesday, Feb 19, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center, Room 4213.03 (Math Thesis Room)
Wednesday, February 19, 6:30-8:00pm
James Geiser
Soundness and the Gödel Undecidability Theorem
The goal of Gödel’s argument that the theory (T) of Peano Arithmetic is not complete, was to show that the Gödel sentences, GG , and it’s negation, are not provable in T, unless T is inconsistent. In this paper we examine the first half of this argument, namely, that from a hypothetical derivation, PGPG, of GG, a derivation, PfPf, can be constructed that ends in a contradiction. We make the observation that the Gödel argument depends on the metatheory concept of representability that, in turn, depends on the metatheory concept of soundness. Our analysis leads to two main observations, the first well know, and the second, a challenge to the standard undecidability argument.
1 – The existence of PGPG implies that T is unsound. This conclusion does not require the further construction, from PGPG, of the derivation PfPf.
2 - We argue that effectuation of the construction of PfPf is obstructed, because that effectuation requires acceptance of a contradiction in the metatheory regarding the soundness of T.
This is joint work with Catherine Hennix.
The New York City Category Theory Seminar
Department of Computer Science, Department of Mathematics
The Graduate Center of The City University of New York
Date and Time: Wednesday February 19, 2020, 7:00 - 8:30 PM., Room 6417.
Speaker: Todd Trimble, Western Connecticut State University.
Title: The Universal Property of the Bar Construction.
Abstract: The bar construction is a fundamental construction used throughout homological algebra and algebraic topology, including for example the construction of classifying bundles, deloopings of suitable H-spaces, and free resolutions of general algebras and the cohomology thereof. The underlying theme is that the bar construction produces canonical contractible or acyclic simplicial algebras, as usually explained by the acyclic models theorem. In this talk we sharpen this result, giving a precise sense in which the bar construction is a universal acyclic simplicial algebra, here recasting "acyclic" not as a property but as an algebraic structure, whereby acyclic structures are coalgebras over the decalage comonad.
- - - - Thursday, Feb 20, 2020 - - - -
- - - - Friday, Feb 21, 2020 - - - -
Logic Workshop
CUNY Graduate Center, Room 6417
Friday, February 21, 2:00-3:30pm
Andrey Morozov, Novosibirsk State UniversityOn ΣΣ-preorderings in HF(R)We prove that ω1ω1 cannot be embedded into any preordering ΣΣ-definable with parameters in the hereditarily finite superstructure over the ordered field of real numbers, HF(R). As corollaries, we obtain characterizations of ΣΣ-presentable ordinals and Gödel constructive sets of kind LαLα. It also follows that there are no ΣΣ-presentations for structures of TT-, mm-, 11-, and tttt-degrees over HF(R).
- - - - Other Logic News - - - -
CONFERENCE ANNOUNCEMENT:
The “Sao Paulo School of Advanced Science on Contemporary Logic, Rationality and Information - SPLogIC”, sponsored by FAPESP and promoted by the Centre for Logic, Epistemology and the History of Science (CLE) of the University of Campinas (Unicamp), Brazil, will be held at Unicamp from July 13th to 24th, 2020.
The School celebrates the 90th anniversary of Newton da Costa and aims at: providing an overview of the state-of-art methodology and research on contemporary logic (featuring non-classical logics), rationality, and information.
The program comprises 9 courses and 9 plenary talks delivered in English by experts in each topic, as well as oral presentations (LED Talks) and poster sessions by the students.
Topics to be covered include:
• History and Philosophy of Paraconsistent Logics
• The Australian, Belgian, Brazilian, and Israeli schools on paraconsistency
• Logic and Reasoning, Logic and Information, Logic and Argumentation
• Methodological aspects on interpreting, translating and combining logics
• Logic, Probability and Artificial Intelligence.
The event will select 100 fully-funded participants (50 grantees from all states of Brazil and 50 international grantees). Funding includes airfare, medical insurance, accommodation and meals throughout the two weeks.
Undergraduate students, graduate students and postdoctoral fellows (up to 5 years after completion of the Ph.D) from all countries are encouraged to apply.
Applications are open from January 15th to February 22th, 2020.
More information and Call for Applications at https://splogic.org.
- - - - Web Site - - - -
Find us on the web at:
nylogic.github.io(site designed, built & maintained by Victoria Gitman)
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Wednesday seminar
Prague Set Theory Seminar
2/7/2020
Dear all,
The seminar meets on Wednesday February 12th at 11:00 in the Institute
of Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.
Program: The program is not yet determined, presumably either Jonathan
Verner or I will talking about something.
Best,
David
Udine Workshop on Singular Cardinals, Udine, Italy, July 6-7, 2020
Conference
2/7/2020
Udine Workshop on Singular Cardinals
We are happy to announce the upcoming "Udine Workshop on Singular Cardinals", that will be held in Udine (Italy) on 6-7 July 2020. It will be held at Palazzo di Toppo Wassermann, a prestigious 18th-century palace. Singular cardinals are transversal to set theory and beyond, and this will be an occasion to bring together researchers working on singular cardinals and share the latest developments on this topic.
Organizers:
Vincenzo Dimonte (University of Udine)
Mirna Dzamonja (The University of East Anglia)
Luca Motto Ros (University of Torino)
Talks:
James Cummings (Carnegie Mellon University)
Péter Komjáth (Eötvös Loránd University)
Menachem Magidor (The Hebrew University of Jerusalem) *
Itay Neeman (UCLA) *
Assaf Rinot (Bar-Ilan University)
Jouko Väänänen (University of Helsinki)
* To confirm
Website: https://users.dimi.uniud.it/~vincenzo.dimonte/WSC2020.html
There will be some slots open for contributed talks, and all the interested researchers and students are encouraged to apply. To propose a contributed talk, please write to vincenzo.dimonte@uniud.it by May the 31st.
For further information, contact vincenzo.dimonte@uniud.it
Tagged: James Cummings, Péter Komjáth, Menachem Magidor, Itay Neeman, Assaf Rinot, Jouko Väänänen
(KGRC) research seminar talk on WEDNESDAY, February 12
Kurt Godel Research Center
2/6/2020
The KGRC welcomes as guests:
Jana Marikova (host: Benjamin Miller) will stay until June 30.
Clifton Ealy (host: Benjamin Miller) will visit from March 7 to March 15 and
from May 9 to June 30.
Miguel Moreno (host: Lyubomyr Zdomskyy) will stay until November 30.
Vincenzo Dimonte (host: Sy-David Friedman) will stay from February 8 to
February 13 and give a talk on February 12 (see below).
Martin Zeman (hosts: Sandra Müller and Monroe Eskew) will visit end of February
or early March (to be determined) and give a talk on March 5 (tentative date).
Jerzy Kakol (host: Damian Sobota) will stay from March 29 to April 4 and give a
talk on April 2.
Chi Tat Chong (host: Sy-David Friedman) will stay from June 17 to June 19 and
give a talk on June 18.
* * *
Research seminar
Kurt Gödel Research Center
WEDNESDAY, February 12
(Please note the unusual day.)
"Regularity properties in singular generalized descriptive set theory"
Vincenzo Dimonte (University of Udine, Italy)
Generalized descriptive set theory is the study of definable subsets of the
space ${}^\kappa 2$ with the bounded topology. Such study has been
overwhelmingly focussed on the case with $\kappa$ regular. Motivated by the
theory of rank-into-rank cardinals, we concentrated instead on the case of
$\kappa$ singular of cofinality $\omega$, painting a picture that is quite
similar to the classical descriptive set theory case. This talk is going to
center around the generalization of regularity properties (Perfect Set Property
and Baire Property) in this context. The PSP is still akin to the classical
case, while the BP probably needs more large-cardinal power to be non-trivial.
Time and Place
Tea at 3:30pm in the KGRC meeting room (seminar room CST5.47)
Talk at 4:00pm in the KGRC lecture room (seminar room D5.48)
Universität Wien
Institut für Mathematik
Kurt Gödel Research Center
Augasse 2-6, UZA 1 - Building 2
1090 Wien
This Week in Logic at CUNY
This Week in Logic at CUNY
2/3/2020
Hi everyone,
This is the first edition of "This Week in Logic" in this new semester and new decade - welcome back! Future mailings will occur weekly on Sunday evenings.
Best,
Jonas Reitz
This Week in Logic at CUNY:
- - - - Tuesday, Feb 4, 2020 - - - -
- - - - Wednesday, Feb 05, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center, Room 4213.03 (Math Thesis Room)
Wednesday, Feb 5, 6:30-8:00pm
Athar Abdul-Quader, Purchase CollegeThe pentagon saga continues
I will continue to speak about Jim Schmerl's recent paper on the pentagon lattice N5N5. In this talk, I will outline the main result that no model of PA has a 'mixed' elementary extension such that the resulting interstructure lattice is isomorphic to the pentagon.
- - - - Thursday, Feb 06, 2020 - - - -
- - - - Friday, Feb 07, 2020 - - - -
Logic Workshop
CUNY Graduate Center, Room 6417
Friday, Feb 7, 2:00-3:30pm
Victor Selivanov, Institute of Informatics Systems, Novosibirsk
A Q-Wadge hierarchy in quasi-Polish spaces
The Wadge hierarchy was originally defined and studied only in the Baire space (and some other zero-dimensional spaces). We extend it to arbitrary topological spaces by providing a set-theoretic definition of all its levels. We show that our extension behaves well in second countable spaces and especially in quasi-Polish spaces. In particular, all levels are preserved by continuous open surjections between second countable spaces, which implies, e.g., several Hausdorff-Kuratowski-type theorems in quasi-Polish spaces. In fact, many results hold not only for the Wadge hierarchy of sets but also for its extension to Borel functions from a space to a countable better quasiorder Q.
Next Week in Logic at CUNY:
- - - - Monday, Feb 10, 2020 - - - -
Logic and Metaphysics Workshop
Date: Monday, February 10, 4.15-6.15
Place: Room 7395, CUNY Graduate Center
Melissa Fusco (Columbia).
Title: A Deontic Logic for Two Paradoxes of Deontic Modality
Abstract: In this paper, we take steps towards axiomatizing the two dimensional deontic logic in Fusco (2015), which validates a form of free choice permission (von Wright 1969, Kamp 1973; (1) below) and witnesses the nonentailment known as Ross’s Puzzle (Ross 1941; (2) below).
(1) You may have an apple or a pear ⇒ You may have an apple, and you may have a pear.
(2) You ought to post the letter = ̸⇒ You ought to post the letter or burn it.
Since <>(p or q) = (<>p ∨ <>q) and [ ](p) ⇒ [ ](p ∨ q) are valid in any normal modal logic – including standard deontic logic – the negations of (1)-(2) are entrenched in modal proof systems. To reverse them without explosion will entail excavating the foundations of the propositional tautologies. The resulting system pursues the intuition that classical tautologies involving disjunctions are truths of meaning, rather than propositional necessities. This marks a departure from the commitments the propositional fragment of a modal proof system is standardly taken to embody.
Note: This is joint work with Arc Kocurek (Cornell).
- - - - Tuesday, Feb 11, 2020 - - - -
- - - - Wednesday, Feb 12, 2020 - - - -
The New York City Category Theory Seminar
Department of Computer Science, Department of Mathematics
The Graduate Center of The City University of New York
Speaker: Tai-Danae Bradley, The Graduate Center, CUNY.
Date and Time: Wednesday February 12, 2020, 7:00 - 8:30 PM., Room 6417.
Title: TBA.
Abstract: TBA.
- - - - Thursday, Feb 13, 2020 - - - -
- - - - Friday, Feb 14, 2020 - - - -
- - - - Other Logic News - - - -
- - - - Web Site - - - -
Find us on the web at:
nylogic.github.io(site designed, built & maintained by Victoria Gitman)
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Set theory seminar this week: Assaf Shani
Toronto Set Theory Seminar
2/3/2020
Hi everyone,
This week Assaf Shani from Carnegie Mellon University will speak in the seminar. His talk is entitled "Borel reducibility and symmetric models."
Abstract: We develop a correspondence between Borel equivalence relations induced by closed subgroups of

and symmetric models of set theory without choice, and apply it to prove a conjecture of Hjorth-Kechris-Louveau (1998). For example, we show that the equivalence relation

is strictly below

in Borel reducibility. By results of Hjorth-Kechris-Louveau,

bounds the complexity of

actions of

, while

bounds the complexity of

actions of "well behaved'' closed subgroups of

, such as abelian groups. The notions mentioned above will be defined in the talk, and I will also survey the results of Hjorth-Kechris-Louveau.
The talk will be held on Friday, February 7 in Fields 210 from 1:30 to 3:00. If you will attend the talk, please register using the following link:
Thanks,
Bill Chen
Logic Seminar 12 Feb 2020 17:00 hrs at NUS
NUS Logic Seminar
2/3/2020
Invitation to the Logic Seminar at the National University of Singapore
Date: Wednesday, 12 February 2020, 17:00 hrs
Room: S17#04-06, Department of Mathematics, NUS
Speaker: Ashutosh Kumar
Title: On some problems in set-theoretic Eucildean Ramsey theory
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Abstract: We shall discuss some questions in Euclidean Ramsey theory where
techniques from set theory have played a role.
Wednesday seminar
Prague Set Theory Seminar
1/30/2020
Dear all,
The seminar meets on Wednesday February 5th at 11:00 in the Institute of
Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.
We will have quests speakers from Morelia. The main program is:
César Corral -- Frechet-like properties in almost disjoint families
Abstract: We will study some strong Frechet properties and properties
very related to the preservation of Frechetness under products. Our main
tool to construct counterexamples to some implications between them will
be the use of almost disjoint families.
Time permitting, there might be more topics/speakers.
Best,
David
Tagged: César Corral
Logic Seminar
Barcelona Logic Seminar
1/29/2020 10:09:59
Next session of the Logic Seminar
Asaf Karagila
Newton International Fellow, School of Mathematics, UEA (Norwich)
THE POWER OF POWER SETS OF COUNTABLE UNIONS OF COUNTABLE SETS
Wednesday, February 5.
12:30
IMUB Lecture Room, Facultat de Matemàtiques i Informàtica, UB.
http://www.ub.edu/slb/Seminar.html
Aquest missatge, i els fitxers adjunts que hi pugui haver, pot contenir informació confidencial o protegida legalment i s’adreça exclusivament a la persona o entitat destinatària. Si no consteu com a destinatari final
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que hi pugui haver.
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de recibirlo, no está autorizado a leerlo, retenerlo, modificarlo, distribuirlo o copiarlo, ni a revelar su contenido. Si lo ha recibido por error, informe de ello al remitente y elimine del sistema tanto el mensaje como los ficheros adjuntos que pueda contener.
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Re: Set Theory Seminar
Barcelona Set Theory Seminar
1/24/2020
Dear Colleagues,
Please find attached the announcement of the next session of the Barcelona Set Theory seminar.
You are all welcome to attend.
Best regards,
Joan
Joan Bagaria 🎗
ICREA Research Professor
Universitat de Barcelona
Departament de Matemàtiques i Informàtica
Gran Via de les Corts Catalanes 585
08007 Barcelona
Catalonia
Phone: +34 93 402 1609
Eduardo Sealtiel Martínez Mendoza: Teoría PCF e hipótesis del continuo generalizada revisada
Mexico City Logic Seminar
1/24/2020
Con la teoría de las posibles cofinalidades de Shelah tenemos una herramienta que nos permite estudiar a más profundidad la operación de exponenciación cardinal. Uno de los resultados más destacados que podemos obtener a partir de esta teoría es que si 2^{\aleph_0}<\aleph_{\omega_4}, entonces \aleph_{\omega}^{\aleph_0}<\aleph_{\omega_4}. Otro resultado igual de interesante está relacionado con uno de los problemas centrales de teoría de conjuntos.
Sabemos que la hipótesis del continuo generalizada es equivalente a que para cualesquiera cardinales regulares \lambda>\kappa, \lambda^\kappa=\lambda.. Este enunciado se puede aproximar a partir del nivel de cualquier cardinal límite fuerte si consideramos una modificación de la operación de exponenciación cardinal. A esta aproximación se le llama hipótesis del continuo generalizada revisada de Shelah, la cual tiene como consecuencias algunos resultados de carácter combinatorio. Por ejemplo, a partir del primer cardinal límite fuerte, la hipótesis del continuo generalizada es equivalente al principio diamante de Jensen. También, podemos acotar a la celularidad de algunas álgebras booleana con cardinales específicos.
Tagged: Eduardo Sealtiel Martínez Mendoza
Logic Seminar Wed 29 Jan 2020 17:00 hrs at NUS - Talk by Wang Wei
NUS Logic Seminar
1/22/2020
Invitation to the Logic Seminar at the National University of Singapore
Date: Wednesday, 29 January 2019, 17:00 hrs
Room: S17#04-06, Department of Mathematics, NUS
Speaker: Wang Wei, Sun Yat-Sen University, Guangzhou
Title: Non-standard models of arithmetic and their standard systems.
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Abstract:
PA is the first order fragment of Peano's axiomatization of the natural
numbers. The natural numbers, N, is called the standard model of PA. But by
compactness theorem in first order logic, there are also models of PA
different from N, which are called non-standard models of arithmetic. Like
in N, every element of a non-standard model M has a binary expansion, which
can be regarded as the characteristic function of a subset of N. The
standard system of M is the collection of all such subsets of N. It is
known that standard systems of non-standard models are always Scott sets
and every Scott set of cardinality less than or equal to the first
uncountable cardinal is the standard system of some non-standard model.
However, the general Scott set problem, whether every Scott set is the
standard system of some non-standard model, remains one of the major open
problems in the model theory of arithmetic. This talk will present some
history of Scott set problem, as well as two constructions of non-standard
models with uncountable standard systems.
Tagged: Wang Wei
Set Theory Seminar in the Stewart Library this week
Toronto Set Theory Seminar
1/22/2020
Hi everyone,
After some negotiation, we were upgraded to the Stewart Library on the third floor for this week. Here is the info:
Speaker: Henry Yuen
Title: Connes' Embedding Problem through the lens of complexity theory
Location: Fields Institute Stewart Library (#309)
Date and time: Friday, January 24 2020, 1:30-3:00.
Thanks,
Bill
Wednesday seminar
Prague Set Theory Seminar
1/22/2020
Dear all,
There is no seminar next week, Wednesday January 29th, there are however
still spots to participate the Winter School next week.
https://www.winterschool.eu/
The seminars in February are to be decided.
No announcement = no seminar.
Best,
David
(KGRC) research seminar talk on Thursday, January 30
Kurt Godel Research Center
1/22/2020
The KGRC welcomes as guests:
Jana Marikova (host: Benjamin Miller) will stay until June 30.
Clifton Ealy (host: Benjamin Miller) will visit from March 7 to March 15
and from May 9 to June 30.
Miguel Moreno (host: Lyubomyr Zdomskyy) will stay until November 30 and
give a talk on January 23.
Leandro Aurichi (host: Lyubomyr Zdomskyy) will stay until January 31.
Jerzy Kakol (host: Damian Sobota) will stay from March 29 to April 4 and
give a talk on April 2.
Chi Tat Chong (host: Sy-David Friedman) will stay from June 17 to June 19
and give a talk on June 18.
* * *
Research seminar
Kurt Gödel Research Center Thursday, January 30
"Construction with opposition: Cardinal invariants and games"
Víctor Torres-Pérez (TU Wien)
We consider several game versions of the cardinal invariants $\mathfrak t$,
$\mathfrak u$ and $\mathfrak a$. We show that the standard proof that
parametrized diamond principles prove that the cardinal invariants are small
actually shows that their game counterparts are small. On the other hand we
show that $\mathfrak t < \mathfrak t_{Builder}$ and $\mathfrak u < \mathfrak
u_{Builder}$ are both relatively consistent with ZFC, where $\mathfrak
t_{Builder}$ and $\mathfrak u_{Builder}$ are the principal game versions of
$\mathfrak t$ and $\mathfrak u$, respectively. The corresponding question for
$\mathfrak a$ remains open.
This is a joint work with Jörg Brendle and Michael Hru\v{s}'ak.
Time and Place
Tea at 3:30pm in the KGRC meeting room (seminar room CST5.47)
Talk at 4:00pm in the KGRC lecture room (seminar room D5.48)
Universität Wien
Institut für Mathematik
Kurt Gödel Research Center
Augasse 2-6, UZA 1 - Building 2
1090 Wien
Set theory seminar next week: Henry Yuen
Toronto Set Theory Seminar
1/17/2020
Hi everyone,
The talk will be held on Friday, January 24 in the Fields Institute from 1:30 to 3:00.
I expect that the seminar will be of broad interest, so please invite your colleagues working in relevant areas to attend. If you will attend the talk, please register using the following link
http://www.surveygizmo.com/s3/3247294/Seminar-Registration and send me a reply email indicating your interest, so that I can secure a larger room than our usual meeting place (Fields 210) if needed.
See you there,
Bill Chen
Tagged: Henry Yuen
Set theory seminar tomorrow: Spencer Unger
Toronto Set Theory Seminar
1/16/2020
Hi everyone,
This week Spencer Unger will speak in the seminar. IMPORTANT: note the change in time and place!
The talk will be held on Friday, January 17 in Huron 1018 from 10:00 to 11:00. If you will attend the talk, please register using the following link:
Location: the Huron Building is located on Huron Street adjacent to the Fields Institute and the Bahen Centre. Our room is a seminar room located on the 10th floor. To access this room, please take the elevator to the 9th floor and then walk up one flight of stairs. I will leave from the Fields Institute to the seminar location shortly before the seminar begins.
See you there,
Bill Chen
Tagged: Spencer Unger
Wednesday seminar
Prague Set Theory Seminar
1/14/2020
Dear all,
There is no seminar tomorrow Wednesday January 15th.
The seminar meets again next week, Wednesday January 22nd at 11:00 in
the Institute of Mathematics CAS, Zitna 25, seminar room, 3rd floor,
front building.
Program: Egbert Thümmel will speak about omega_1 injective ideals in
Boolean algebras, and Jan Šaroch will talk about applications of
injective ideals (and set theory in general) in abstract algebra (modules).
Best,
David
Tagged: Egbert Thümmel
(KGRC) PhD defense and other upcoming talks
Kurt Godel Research Center
1/14/2020
The KGRC welcomes as guests:
Jana Marikova (host: Benjamin Miller) will stay until June 30, 2020.
Clifton Ealy (host: Benjamin Miller) will stay until January 11, then
visit again March 7 to March 15 and May 9 to June 30.
Miguel Moreno (host: Lyubomyr Zdomskyy) will stay until November 30, 2020
and give a talk on January 23 (see below).
Corey Switzer (host: Vera Fischer) will stay from January 12 to January 19
and give a talk on January 16 (see below).
Leandro Aurichi (host: Lyubomyr Zdomskyy) will stay from January 15 to
January 31.
Jerzy Kąkol (host: Damian Sobota) will stay from March 29 to April 4 and give a
talk on April 2.
Chi Tat Chong (host: Sy-David Friedman) will give a talk on June 18, 2020.
* * *
PhD Defense
Kurt Gödel Research Center
Wednesday, January 15
"Generalized notions of recurrence: Bases and the
existence of invariant probability measures"
Jürgen Manuel Inselmann (KGRC)
We establish basis and anti-basis theorems for a broad collection of recurrence
notions appearing in descriptive, measurable, and topological dynamics, and
show that such notions cannot characterize the existence of invariant
probability measures in the deacriptive milieu.
Time and Place
Talk at 10:00am in the KGRC lecture room (seminar room D5.48)
Universität Wien
Institut für Mathematik
Kurt Gödel Research Center
Augasse 2-6, UZA 1 - Building 2
1090 Wien
* * *
Research seminar
Kurt Gödel Research Center
Thursday, January 16
"Generalized Cardinal Characteristics for Sets of Functions"
Corey Bacal Switzer (City University of New York, Graduate Center, USA)
Cardinal characteristics on the generalized Baire and Cantor spaces
$\kappa^\kappa$ and $2^\kappa$ have recently generated significant interest. In
this talk I will introduce a different generalization of cardinal
characteristics, namely to the space of functions $f:\omega^\omega \to
\omega^\omega$. Given an ideal $\mathcal I$ on Baire space and a relation $R$
let us define $f R_{\mathcal I} g$ for $f$ and $g$ functions from
$\omega^\omega$ to $\omega^\omega$ if and only if $f(x) R g(x)$ for an
$\mathcal I$-measure one set of $x \in \omega^\omega$. By letting $\mathcal I$
vary over the null ideal, the meager ideal and the bounded ideal; and $R$ vary
over the relations $\leq^*$, $\neq^*$ and $\in^*$ we get 18 new cardinal
characteristics by considering the bounding and dominating numbers for these
relations. These new cardinals form a diagram of provable implications similar
to the Cichoń diagram. They also interact in several surprising ways with the
cardinal characteristics on $\omega$. For instance, they can be arbitrarily
large in models of CH, yet they can be $\aleph_1$ in models where the continuum
is arbitrarily large. They are bigger in the Sacks model than the Cohen model.
I will introduce these cardinals, show some of the provable implications and
discuss what is known about consistent inequalities, including new
generalizations of well-known forcing notions on the reals to this context.
This includes joint work with Jörg Brendle.
Time and Place
Tea at 3:30pm in the KGRC meeting room (seminar room CST5.47)
Talk at 4:00pm in the KGRC lecture room (seminar room D5.48)
Universität Wien
Institut für Mathematik
Kurt Gödel Research Center
Augasse 2-6, UZA 1 - Building 2
1090 Wien
* * *
Research seminar
Kurt Gödel Research Center
Thursday, January 23
"Fake Reflection"
Miguel Moreno (Bar-Ilan University, Ramat Gan, Tel Aviv, Israel)
Motivated from many results in generalized descriptive set theory, Filter
Reflection (aka Fake Reflection) is an abstract version of reflection
compatible with large cardinals, forcing axioms, but also V=L.
In this talk we will present the motivation and definition of filter
reflection, we will explain how to force filter reflection and how to
force its failure. We will also show some applications and properties of
filter reflection, e.g. the consistency of "$E_{\omega_1}^\kappa$ filter
reflects to a subset of $E_{\omega}^\kappa$".
Time and Place
Tea at 3:30pm in the KGRC meeting room (seminar room CST5.47)
Talk at 4:00pm in the KGRC lecture room (seminar room D5.48)
Universität Wien
Institut für Mathematik
Kurt Gödel Research Center
Augasse 2-6, UZA 1 - Building 2
1090 Wien
Colloquium this week: Spencer Unger
Toronto Set Theory Seminar
1/13/2020
Hi everyone,
There will be a special colloquium this week given by Spencer Unger of the Hebrew University entitled "A constructive solution to Tarski's circle squaring problem."
The talk will be held in Bahen Centre 6183 on Wednesday, January 15 at 4:00 pm.
https://seminars.math.toronto.edu/seminars/list/events.py/process?start
Stay tuned for updates on Friday's seminar.
Bill
Logic Seminars 15 and 22 January 2020 at NUS
NUS Logic Seminar
1/13/2020
Invitation to the Logic Seminar at the National University of Singapore
(1) Date: Wednesday, 15 January 2020, 17:00 hrs
Room: S17#04-06, Department of Mathematics, NUS
Speaker: Frank Stephan
Title: Measure and Conquer for Max Hamming Distance XSAT
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Abstract:
This talk gives an overview of the joint work of the speaker's
recent work on the Hamming XSAT problem. This problem asks for an
algorithm to determine which, given an XSAT instance, determines
the maximum Hamming distance between two solutions of this instance.
The problem has been studied by Dahloef in 2005 in an ISAAC paper
who provided an O(1.83848^n) algorithm for this problem.
Later Fu, Zhu and Yin presented at JFCST 2012 an O(1.6760^n)
algorithm for the related Max Hamming X3SAT problem where all clauses
have at most three literals. The current paper provides for the
general Max Hamming XSAT problem an O(1.4983^n) algorithm
which applies also the technique "Measure and Conquer"
in order to prove a better bound than the algorithm would give
otherwise. Furthermore, the algorithm does not only provide the
maximum Hamming distance of two solutions of the instance, but
instead for each k between 0 and n the number
of pairs of solutions which have Hamming distance k.
For the special case Max Hamming Distant X3SAT, Hoi, Jain and Stephan
have the bound O(1.3298^n) at the conference FSTTCS 2019.
(2) Date: Wednesday, 22 January 2020, 17:00 hrs
Room: S17#04-06, Department of Mathematics, NUS
Speaker: Asger Dag Toernquist, Kobenhavns Universitet
Title: Mad, med, mcg and other maximal combinatorial objects.
URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html
Abstract:
This talk is about the descriptive set theory and infinitary combinatorics.
In the past 6 years, a number of long-standing problems related to the
definability (in the sense of effective descriptive set theory) of
so-called maximal almost disjoint (mad) families, maximal eventually
different (med) families, and maximal cofinitary groups (mcg) have been
solved by an array of authors. I will give an overview of these developments.
Almost disjoint families are families of infinite subsets of omega
where any two distinct elements of the family intersect finitely;
eventually different families are families of functions from omega to omega
such that any two distinct functions in the family are eventually different;
and cofinitary groups are subgroups of the group of all permutations of omega
with the property that all non-identity elements of the group have at most
finitely many fixed points. Maximality of such objects in all cases means
maximal under inclusion (among such families).
A classical result due to Adrian Mathias states that no analytic infinite
mad families. A slew of recent results shed light on this classical
result by showing that under suitable descriptive set-theoretic
regularity assumptions, there are no mad families at all (and this
localizes to suitable pointclasses, especially to analytic sets).
In a totally unexpected twist, Horowitz and Shelah showed in 2016
that there are Borel med families and mcg, solving a long-standing
problem. I will finish the talk by discussing some related, still
unsolved problems, especially the following: Is there a maximal
(infinite) analytic set of pairwise Turing-incomparable reals?
Wednesday seminar
Prague Set Theory Seminar
1/3/2020
Dear all,
The seminar meets on Wednesday January 8th at 11:00 in the Institute of
Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.
The program is not yet determined, walk-in speakers will be welcome.
Best,
David